diff --git a/DESCRIPTION b/DESCRIPTION
index 55066cb..d9acf9d 100755
--- a/DESCRIPTION
+++ b/DESCRIPTION
@@ -1,6 +1,6 @@
 Package: SBC
 Title: Simulation Based Calibration for rstan/cmdstanr models
-Version: 0.1.1.9000
+Version: 0.2.0.9000
 Authors@R: 
     c(person(given = "Shinyoung",
            family = "Kim",
diff --git a/NAMESPACE b/NAMESPACE
index 9371fe2..e3fb7cf 100755
--- a/NAMESPACE
+++ b/NAMESPACE
@@ -90,6 +90,7 @@ export(SBC_print_example_model)
 export(SBC_results)
 export(SBC_statistics_from_single_fit)
 export(bind_datasets)
+export(bind_derived_quantities)
 export(bind_generated_quantities)
 export(bind_results)
 export(calculate_prior_sd)
@@ -98,11 +99,13 @@ export(calculate_sds_draws_matrix)
 export(check_all_SBC_diagnostics)
 export(cjs_dist)
 export(compute_SBC)
+export(compute_dquants)
 export(compute_gen_quants)
 export(compute_results)
 export(data_for_ecdf_plots)
 export(default_chunk_size)
 export(default_cores_per_fit)
+export(derived_quantities)
 export(draws_rvars_to_standata)
 export(draws_rvars_to_standata_single)
 export(empirical_coverage)
@@ -123,6 +126,7 @@ export(recompute_statistics)
 export(set2set)
 export(validate_SBC_datasets)
 export(validate_SBC_results)
+export(validate_derived_quantities)
 export(validate_generated_quantities)
 export(wasserstein)
 import(ggplot2)
diff --git a/R/derived-quantities.R b/R/derived-quantities.R
new file mode 100644
index 0000000..4a366d7
--- /dev/null
+++ b/R/derived-quantities.R
@@ -0,0 +1,162 @@
+#' Create a definition of derived quantities evaluated in R.
+#'
+#' When the expression contains non-library functions/objects, and parallel processing
+#' is enabled, those must be
+#' named in the `.globals` parameter (hopefully we'll be able to detect those
+#' automatically in the future). Note that [recompute_SBC_statistics()] currently
+#' does not use parallel processing, so `.globals` don't need to be set.
+#'
+#' @param ... named expressions representing the quantitites
+#' @param .globals A list of names of objects that are defined
+#' in the global environment and need to present for the gen. quants. to evaluate.
+#' It is added to the `globals` argument to [future::future()], to make those
+#' objects available on all workers.
+#' @examples
+#'# Derived quantity computing the total log likelihood of a normal distribution
+#'# with known sd = 1
+#'normal_lpdf <- function(y, mu, sigma) {
+#'  sum(dnorm(y, mean = mu, sd = sigma, log = TRUE))
+#'}
+#'
+#'# Note the use of .globals to make the normal_lpdf function available
+#'# within the expression
+#'log_lik_dq <- derived_quantities(log_lik = normal_lpdf(y, mu, 1),
+#'                                 .globals = "normal_lpdf" )
+#'
+#' @export
+derived_quantities <- function(..., .globals = list()) {
+  structure(rlang::enquos(..., .named = TRUE),
+            class = "SBC_derived_quantities",
+            globals = .globals
+            )
+}
+
+#' @title Validate a definition of derived quantities evaluated in R.
+#' @export
+validate_derived_quantities <- function(x) {
+  # Backwards compatibility
+  if(inherits(x, "SBC_generated_quantities")) {
+    class(x) <- "SBC_derived_quantities"
+  }
+  stopifnot(inherits(x, "SBC_derived_quantities"))
+  invisible(x)
+}
+
+#' @title Combine two lists of derived quantities
+#' @export
+bind_derived_quantities <- function(dq1, dq2) {
+  validate_derived_quantities(dq1)
+  validate_derived_quantities(dq2)
+  structure(c(dq1, dq2),
+            class = "SBC_derived_quantities",
+            globals = bind_globals(attr(dq1, "globals"), attr(dq2, "globals")))
+}
+
+#'@title Compute derived quantities based on given data and posterior draws.
+#'@param gen_quants Deprecated, use `dquants`
+#'@export
+compute_dquants <- function(draws, generated, dquants, gen_quants = NULL) {
+  if(!is.null(gen_quants)) {
+    warning("gen_quants argument is deprecated, use dquants")
+    if(rlang::is_missing(dquants)) {
+      dquants <- gen_quants
+    }
+  }
+  dquants <- validate_derived_quantities(dquants)
+  draws_rv <- posterior::as_draws_rvars(draws)
+
+  draws_env <- list2env(draws_rv)
+  if(!is.null(generated)) {
+    if(!is.list(generated)) {
+      stop("compute_dquants assumes that generated is a list, but this is not the case")
+    }
+    generated_env <- list2env(generated, parent = draws_env)
+
+    data_mask <- rlang::new_data_mask(bottom = generated_env, top = draws_env)
+  } else {
+    data_mask <- rlang::new_data_mask(bottom = draws_env)
+  }
+
+  eval_func <- function(dq) {
+    # Wrap the expression in `rdo` which will mostly do what we need
+    # all the tricks are just to have the correct environment when we need it
+    wrapped_dq <- rlang::new_quosure(rlang::expr(posterior::rdo(!!rlang::get_expr(dq))), rlang::get_env(dq))
+    rlang::eval_tidy(wrapped_dq, data = data_mask)
+  }
+  rvars <- lapply(dquants, FUN = eval_func)
+  do.call(posterior::draws_rvars, rvars)
+}
+
+
+
+#' @title Create a definition of derived quantities evaluated in R.
+#' @description Delegates directly to `derived_quantities()`.
+#'
+#' @name generated_quantities-deprecated
+#' @seealso \code{\link{SBC-deprecated}}
+#' @keywords internal
+NULL
+
+#' @rdname SBC-deprecated
+#' @section \code{generated_quantities}:
+#' Instead of \code{generated_quantities}, use \code{\link{derived_quantities}}.
+#'
+#' @export
+generated_quantities <- function(...) {
+  warning("generated_quantities() is deprecated, use derived_quantities instead.")
+  derived_quantities(...)
+}
+
+#' @title Validate a definition of derived quantities evaluated in R.
+#' @description Delegates directly to `validate_derived_quantities()`.
+#'
+#' @name generated_quantities-deprecated
+#' @seealso \code{\link{SBC-deprecated}}
+#' @keywords internal
+NULL
+
+#' @rdname SBC-deprecated
+#' @section \code{validate_generated_quantities}:
+#' Instead of \code{validate_generated_quantities}, use \code{\link{validate_derived_quantities}}.
+#'
+#' @export
+validate_generated_quantities <- function(...) {
+  warning("generated_quantities() is deprecated, use validate_derived_quantities instead.")
+  validate_derived_quantities(...)
+}
+
+#' @title Combine two lists of derived quantities
+#' @description Delegates directly to `bind_derived_quantities()`.
+#'
+#' @name bind_generated_quantities-deprecated
+#' @seealso \code{\link{SBC-deprecated}}
+#' @keywords internal
+NULL
+
+#' @rdname SBC-deprecated
+#' @section \code{bind_generated_quantities}:
+#' Instead of \code{bind_generated_quantities}, use \code{\link{bind_derived_quantities}}.
+#'
+#' @export
+bind_generated_quantities <- function(...) {
+  warning("bind_generated_quantities() is deprecated, use bind_derived_quantities instead.")
+  bind_derived_quantities(...)
+}
+
+#'@title Compute derived quantities based on given data and posterior draws.
+#' @description Delegates directly to `compute_dquants()`.
+#'
+#' @name compute_gen_quants-deprecated
+#' @seealso \code{\link{SBC-deprecated}}
+#' @keywords internal
+NULL
+
+#' @rdname SBC-deprecated
+#' @section \code{compute_gen_quants}:
+#' Instead of \code{compute_gen_quants}, use \code{\link{compute_dquants}}.
+#'
+#' @export
+compute_gen_quants <- function(...) {
+  warning("compute_gen_quants() is deprecated, use compute_dquants() instead.")
+  compute_dquants(...)
+}
diff --git a/R/results.R b/R/results.R
index c3d5c05..d5a4223 100644
--- a/R/results.R
+++ b/R/results.R
@@ -254,7 +254,8 @@ length.SBC_results <- function(x) {
               errors = x$errors[indices])
 }
 
-#' Bind globals used in gen quants or backend
+#' Combine two sets globals for use in derived quantities or backend
+#' @seealso [compute_SBC()], [derived_quantities()]
 bind_globals <- function(globals1, globals2) {
     if(length(globals1) > 0 && length(globals2)  > 0) {
       if(is.list(globals1) != is.list(globals2)) {
@@ -365,6 +366,8 @@ compute_results <- function(...) {
 #' @param cache_location The filesystem location of cache. For `cache_mode = "results"`
 #'    this should be a name of a single file. If the file name does not end with
 #'    `.rds`, this extension is appended.
+#' @param dquants Derived quantities to include in SBC. Use [derived_quantities()] to construct them.
+#' @param gen_quants Deprecated, use dquants instead
 #' @param globals A list of names of objects that are defined
 #' in the global environment and need to present for the backend to work (
 #' if they are not already available in package).
@@ -378,15 +381,23 @@ compute_SBC <- function(datasets, backend,
                             thin_ranks = SBC_backend_default_thin_ranks(backend),
                             ensure_num_ranks_divisor = 2,
                             chunk_size = default_chunk_size(length(datasets)),
-                            gen_quants = NULL,
+                            dquants = NULL,
                             cache_mode = "none",
                             cache_location = NULL,
-                            globals = list()) {
+                            globals = list(),
+                            gen_quants = NULL) {
   stopifnot(length(datasets) > 0)
 
-  datasets <- validate_SBC_datasets(datasets)
   if(!is.null(gen_quants)) {
-    gen_quants <- validate_generated_quantities(gen_quants)
+    warning("gen_quants argument is deprecated, use dquants")
+    if(is.null(dquants)) {
+      dquants <- gen_quants
+    }
+  }
+
+  datasets <- validate_SBC_datasets(datasets)
+  if(!is.null(dquants)) {
+    dquants <- validate_derived_quantities(dquants)
   }
 
   ## Handle caching
@@ -410,9 +421,14 @@ compute_SBC <- function(datasets, backend,
 
     if(file.exists(cache_location)) {
       results_from_cache <- readRDS(cache_location)
+      # Ensure backwards compatibility of cache
+      if(!("dquants" %in% names(results_from_cache)) && ("gen_quants" %in% names(results_from_cache))) {
+        # This type of assignment necessary to preserve NULL values
+        results_from_cache["dquants"] <- list(results_from_cache$gen_quants)
+      }
       if(!is.list(results_from_cache) ||
          !all(
-           c("result", "backend_hash", "data_hash", "thin_ranks", "gen_quants","keep_fits")
+           c("result", "backend_hash", "data_hash", "thin_ranks", "dquants","keep_fits")
            %in% names(results_from_cache))) {
         warning("Cache file exists but is in invalid format. Will recompute.")
       } else if(results_from_cache$backend_hash != backend_hash) {
@@ -427,21 +443,31 @@ compute_SBC <- function(datasets, backend,
         result <- tryCatch(validate_SBC_results(results_from_cache$result),
                            error = function(e) { NULL })
 
+        error_dquants <- "error dquants"
+        if(!is.null(results_from_cache$dquants)) {
+          results_from_cache$dquants <-
+            tryCatch(validate_derived_quantities(results_from_cache$dquants),
+                           error = function(e) { error_dquants })
+
+        }
         if(is.null(result)) {
           warning("Cache file contains invalid SBC_results object. Will recompute.")
         } else if(results_from_cache$thin_ranks != thin_ranks ||
-                  !identical(results_from_cache$gen_quants, gen_quants) ||
+                  !identical(results_from_cache$dquants, dquants) ||
                   results_from_cache$ensure_num_ranks_divisor != ensure_num_ranks_divisor)  {
+          if(identical(results_from_cache$dquants, error_dquants)) {
+            warning("dquants loaded from cache are invalid")
+          }
           if(!results_from_cache$keep_fits) {
-            message("Cache file exists, but was computed with different thin_ranks/gen_quants/ensure_num_ranks_divisor and keep_fits == FALSE. Will recompute.")
+            message("Cache file exists, but was computed with different thin_ranks/dquants/ensure_num_ranks_divisor and keep_fits == FALSE. Will recompute.")
           } else {
             message(paste0("Results loaded from cache file '", cache_basename,
-                           "' but it was computed with different thin_ranks/gen_quants/ensure_num_ranks_divisor.\n",
+                           "' but it was computed with different thin_ranks/dquants/ensure_num_ranks_divisor.\n",
                            "Calling recompute_SBC_statistics."))
             return(recompute_SBC_statistics(old_results = result, datasets = datasets,
                                         thin_ranks = thin_ranks,
                                         ensure_num_ranks_divisor = ensure_num_ranks_divisor,
-                                        gen_quants = gen_quants,
+                                        dquants = dquants,
                                         backend = backend))
           }
         } else {
@@ -470,11 +496,11 @@ compute_SBC <- function(datasets, backend,
       generated = datasets$generated[[i]]
     )
   }
-  if(is.null(gen_quants)) {
+  if(is.null(dquants)) {
     future.globals <- globals
   } else {
-    gq_globals <- attr(gen_quants, "globals")
-    future.globals <- bind_globals(globals, gq_globals)
+    dq_globals <- attr(dquants, "globals")
+    future.globals <- bind_globals(globals, dq_globals)
   }
 
   results_raw <- future.apply::future_lapply(
@@ -482,7 +508,7 @@ compute_SBC <- function(datasets, backend,
     backend = backend, cores = cores_per_fit,
     keep_fit = keep_fits, thin_ranks = thin_ranks,
     ensure_num_ranks_divisor = ensure_num_ranks_divisor,
-    gen_quants = gen_quants,
+    dquants = dquants,
     future.seed = TRUE,
     future.globals = future.globals,
     future.chunk.size = chunk_size)
@@ -591,7 +617,7 @@ compute_SBC <- function(datasets, backend,
     results_for_cache <- list(result = res, backend_hash = backend_hash,
                               data_hash = data_hash, thin_ranks = thin_ranks,
                               ensure_num_ranks_divisor = ensure_num_ranks_divisor,
-                              gen_quants = gen_quants, keep_fits = keep_fits)
+                              dquants = dquants, keep_fits = keep_fits)
     tryCatch(saveRDS(results_for_cache, file = cache_location),
              error = function(e) { warning("Error when saving cache file: ", e) })
   }
@@ -679,7 +705,7 @@ reemit_captured <- function(captured) {
 compute_SBC_single <- function(vars_and_generated, backend, cores,
                                keep_fit, thin_ranks,
                                ensure_num_ranks_divisor,
-                               gen_quants) {
+                               dquants) {
 
   variables <- vars_and_generated$variables
   generated <- vars_and_generated$generated
@@ -706,7 +732,7 @@ compute_SBC_single <- function(vars_and_generated, backend, cores,
         res$stats <- SBC::SBC_statistics_from_single_fit(
           res$fit, variables = variables, thin_ranks = thin_ranks,
           ensure_num_ranks_divisor = ensure_num_ranks_divisor,
-          generated = generated, gen_quants = gen_quants,
+          generated = generated, dquants = dquants,
           backend = backend)
 
         res$backend_diagnostics <- SBC::SBC_fit_to_diagnostics(
@@ -752,18 +778,26 @@ compute_SBC_single <- function(vars_and_generated, backend, cores,
 SBC_statistics_from_single_fit <- function(fit, variables, generated,
                                        thin_ranks,
                                        ensure_num_ranks_divisor,
-                                       gen_quants,
-                                       backend) {
+                                       dquants,
+                                       backend,
+                                       gen_quants = NULL) {
+
+  if(!is.null(gen_quants)) {
+    warning("gen_quants argument is deprecated, use dquants")
+    if(rlang::is_missing(dquants)) {
+      dquants <- gen_quants
+    }
+  }
 
   fit_matrix <- SBC_fit_to_draws_matrix(fit)
 
-  if(!is.null(gen_quants)){
-    gen_quants <- validate_generated_quantities(gen_quants)
-    gq_fit <- compute_gen_quants(fit_matrix, generated, gen_quants)
-    fit_matrix <- posterior::bind_draws(fit_matrix, gq_fit, along = "variable")
+  if(!is.null(dquants)){
+    dquants <- validate_derived_quantities(dquants)
+    dq_fit <- compute_dquants(fit_matrix, generated, dquants)
+    fit_matrix <- posterior::bind_draws(fit_matrix, dq_fit, along = "variable")
 
-    gq_variable <- compute_gen_quants(variables, generated, gen_quants)
-    variables <- posterior::bind_draws(variables, gq_variable, along = "variable")
+    dq_variable <- compute_dquants(variables, generated, dquants)
+    variables <- posterior::bind_draws(variables, dq_variable, along = "variable")
   }
 
   shared_vars <- intersect(posterior::variables(variables),
@@ -857,68 +891,6 @@ check_stats <- function(stats, datasets, thin_ranks,
   }
 }
 
-#' Create a definition of generated quantities evaluated in R.
-#'
-#' When the expression contains non-library functions/objects, and parallel processing
-#' is enabled, those must be
-#' named in the `.globals` parameter (hopefully we'll be able to detect those
-#' automatically in the future). Note that [recompute_SBC_statistics()] currently
-#' does not use parallel processing, so `.globals` don't need to be set.
-#'
-#' @param ... named expressions representing the quantitites
-#' @param .globals A list of names of objects that are defined
-#' in the global environment and need to present for the gen. quants. to evaluate.
-#' It is added to the `globals` argument to [future::future()], to make those
-#' objects available on all workers.
-#' @export
-generated_quantities <- function(..., .globals = list()) {
-  structure(rlang::enquos(..., .named = TRUE),
-            class = "SBC_generated_quantities",
-            globals = .globals
-            )
-}
-
-#' @export
-validate_generated_quantities <- function(x) {
-  stopifnot(inherits(x, "SBC_generated_quantities"))
-  invisible(x)
-}
-
-#' @export
-bind_generated_quantities <- function(gq1, gq2) {
-  validate_generated_quantities(gq1)
-  validate_generated_quantities(gq2)
-  structure(c(gq1, gq2),
-            class = "SBC_generated_quantities",
-            globals = bind_globals(attr(gq1, "globals"), attr(gq2, "globals")))
-}
-
-#'@export
-compute_gen_quants <- function(draws, generated, gen_quants) {
-  gen_quants <- validate_generated_quantities(gen_quants)
-  draws_rv <- posterior::as_draws_rvars(draws)
-
-  draws_env <- list2env(draws_rv)
-  if(!is.null(generated)) {
-    if(!is.list(generated)) {
-      stop("compute_gen_quants assumes that generated is a list, but this is not the case")
-    }
-    generated_env <- list2env(generated, parent = draws_env)
-
-    data_mask <- rlang::new_data_mask(bottom = generated_env, top = draws_env)
-  } else {
-    data_mask <- rlang::new_data_mask(bottom = draws_env)
-  }
-
-  eval_func <- function(gq) {
-    # Wrap the expression in `rdo` which will mostly do what we need
-    # all the tricks are just to have the correct environment when we need it
-    wrapped_gq <- rlang::new_quosure(rlang::expr(posterior::rdo(!!rlang::get_expr(gq))), rlang::get_env(gq))
-    rlang::eval_tidy(wrapped_gq, data = data_mask)
-  }
-  rvars <- lapply(gen_quants, FUN = eval_func)
-  do.call(posterior::draws_rvars, rvars)
-}
 
 #' @title Recompute SBC statistics without refitting models.
 #' @description Delegates directly to `recompute_SBC_statistics()`.
@@ -941,7 +913,7 @@ recompute_statistics <- function(...) {
 #' Recompute SBC statistics without refitting models.
 #'
 #' Useful for example to recompute SBC ranks with a different choice of `thin_ranks`
-#' or added generated quantities.
+#' or added derived quantities.
 #' @return An S3 object of class `SBC_results` with updated `$stats` and `$default_diagnostics` fields.
 #' @param backend backend used to fit the results. Used to pull various defaults
 #'   and other setting influencing the computation of statistics.
@@ -950,10 +922,18 @@ recompute_statistics <- function(...) {
 recompute_SBC_statistics <- function(old_results, datasets, backend,
                                  thin_ranks = SBC_backend_default_thin_ranks(backend),
                                  ensure_num_ranks_divisor = 2,
-                                 gen_quants = NULL) {
+                                 dquants = NULL, gen_quants = NULL) {
   validate_SBC_results(old_results)
   validate_SBC_datasets(datasets)
 
+  if(!is.null(gen_quants)) {
+    warning("gen_quants argument is deprecated, use dquants")
+    if(is.null(dquants)) {
+      dquants <- gen_quants
+    }
+  }
+
+
   if(length(old_results) != length(datasets)) {
     stop("The number of fits in old_results does not match the number of simulations")
   }
@@ -976,7 +956,7 @@ recompute_SBC_statistics <- function(old_results, datasets, backend,
                                                         generated = datasets$generated[[i]],
                                                         thin_ranks = thin_ranks,
                                                         ensure_num_ranks_divisor = ensure_num_ranks_divisor,
-                                                        gen_quants = gen_quants,
+                                                        dquants = dquants,
                                                         backend = backend)
       new_stats_list[[i]]$sim_id <- i
       new_stats_list[[i]] <- dplyr::select(new_stats_list[[i]], sim_id, tidyselect::everything())
diff --git a/README.md b/README.md
index 1da10e8..0a11ecd 100755
--- a/README.md
+++ b/README.md
@@ -65,7 +65,7 @@ plot_ecdf_diff(results_sd)
 The diagnostic plots show no problems in this case. As with any other
 software test, we can observe clear failures, but absence of failures does not imply
 correctness. We can however make the SBC check more thorough by using a lot of
-simulations and including suitable generated quantities to guard against
+simulations and including suitable derived quantities to guard against
 [known limitations of vanilla SBC](https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html).
 
 ## Paralellization
@@ -99,7 +99,8 @@ With a little additional work, you can integrate SBC with any exact or approxima
 ## References
 
 * Theoretical support
-   * [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](https://arxiv.org/pdf/1804.06788.pdf) Talts, Betancourt, Simpson, Vehtari, Gelman, 2018
+   * [Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity](https://arxiv.org/abs/2211.02383v1) Modrák, Moon, Kim, Bürkner, Huurre, Faltejsková, Gelman, Vehtari, 2022
+   * [Validating Bayesian Inference Algorithms with Simulation-Based Calibration](http://www.stat.columbia.edu/~gelman/research/unpublished/sbc.pdf) Talts, Betancourt, Simpson, Vehtari, Gelman, 2018
    * [Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison](https://arxiv.org/abs/2103.10522)  Säilynoja, Bürkner, Vehtari, 2021
    * [Bayesian Workflow](https://arxiv.org/abs/2011.01808), Gelman et al., 2020
    * [Toward a principled Bayesian workflow in cognitive science](https://psycnet.apa.org/record/2020-43606-001) Schad, Betancourt, Vasishth, 2021
diff --git a/_pkgdown.yml b/_pkgdown.yml
index 79ac2b3..3e32d1a 100644
--- a/_pkgdown.yml
+++ b/_pkgdown.yml
@@ -90,7 +90,9 @@ reference:
 - contents:
   - compute_SBC
   - contains("SBC_results")
-  - generated_quantities
+  - contains("derived_quantities")
+  - contains("dquants")
+  - bind_globals
   - SBC_statistics_from_single_fit
   - recompute_SBC_statistics
   - bind_results
diff --git a/docs/404.html b/docs/404.html
index 149411c..747d6cc 100644
--- a/docs/404.html
+++ b/docs/404.html
@@ -32,7 +32,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="https://hyunjimoon.github.io/SBC/index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -145,7 +145,7 @@ <h1>Page not found (404)</h1>
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/LICENSE-text.html b/docs/LICENSE-text.html
index cecd59e..dee5374 100644
--- a/docs/LICENSE-text.html
+++ b/docs/LICENSE-text.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -120,7 +120,7 @@ <h1>License</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/LICENSE.html b/docs/LICENSE.html
index bf31acb..940f2a4 100644
--- a/docs/LICENSE.html
+++ b/docs/LICENSE.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -124,7 +124,7 @@ <h1>MIT License</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/articles/SBC.html b/docs/articles/SBC.html
index 1ef2b25..692fac9 100644
--- a/docs/articles/SBC.html
+++ b/docs/articles/SBC.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Getting Started with SBC</h1>
                         <h4 data-toc-skip class="author">Hyunji Moon,
 Martin Modrák, Shinyoung Kim</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/SBC.Rmd" class="external-link"><code>vignettes/SBC.Rmd</code></a></small>
       <div class="hidden name"><code>SBC.Rmd</code></div>
@@ -164,8 +164,8 @@ <h2 id="what-is-sbc">What is SBC?<a class="anchor" aria-label="anchor" href="#wh
 claims like “the posterior 84% credible interval should contain the
 simulated value in 84% of simulations”, the rank uniformity represents
 this claim for all interval widths at once. The theory of SBC is fully
-described in <a href="https://arxiv.org/abs/1804.06788" class="external-link">Talts et
-al.</a></p>
+described in <a href="https://arxiv.org/abs/2211.02383v1" class="external-link">Modrák et
+al.</a> which builds upon <a href="https://arxiv.org/abs/1804.06788" class="external-link">Talts et al.</a></p>
 <p>This opens two principal use-cases of SBC:</p>
 <ol style="list-style-type: lower-alpha">
 <li>We have an algorithm that we trust is correct and a generator and
@@ -426,7 +426,9 @@ <h3 id="computing-ranks">Computing Ranks<a class="anchor" aria-label="anchor" hr
 <code class="sourceCode R"><span><span class="va">results</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">poisson_dataset</span>, <span class="va">poisson_backend</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"results"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'results'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 1 (1%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.015.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 94 (94%) fits had some steps rejected. Maximum number of rejections was 2.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
@@ -439,7 +441,7 @@ <h3 id="viewing-results">Viewing Results<a class="anchor" aria-label="anchor" hr
 </h3>
 <p>We can now inspect the results to see if there were any errors and
 check individual stats:</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results</span><span class="op">$</span><span class="va">stats</span></span></code></pre></div>
 <pre><code><span><span class="co">## <span style="color: #949494;"># A tibble: 100 × 15</span></span></span>
 <span><span class="co">##    sim_id variable simulated_value  rank z_score  mean median    sd   mad    q5</span></span>
@@ -464,13 +466,13 @@ <h3 id="plots">Plots<a class="anchor" aria-label="anchor" href="#plots"></a>
 are uniformly distributed. We can check the rank histogram and ECDF
 plots (see <code><a href="../articles/rank_visualizations.html">vignette("rank_visualizations")</a></code> for description
 of the plots):</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results</span><span class="op">)</span></span></code></pre></div>
 <p><img src="SBC_files/figure-html/rank_hist-1.png" width="700"></p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf</a></span><span class="op">(</span><span class="va">results</span><span class="op">)</span></span></code></pre></div>
 <p><img src="SBC_files/figure-html/ecdf-1.png" width="700"></p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results</span><span class="op">)</span></span></code></pre></div>
 <p><img src="SBC_files/figure-html/ecdf_diff-1.png" width="700"></p>
 <p>Since our simulator and model do match and Stan works well, we see
@@ -550,7 +552,7 @@ <h2 id="acknowledgements">Acknowledgements<a class="anchor" aria-label="anchor"
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/bad_parametrization.html b/docs/articles/bad_parametrization.html
index 2d37169..bed371c 100644
--- a/docs/articles/bad_parametrization.html
+++ b/docs/articles/bad_parametrization.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Discovering bad parametrization with SBC</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/bad_parametrization.Rmd" class="external-link"><code>vignettes/bad_parametrization.Rmd</code></a></small>
       <div class="hidden name"><code>bad_parametrization.Rmd</code></div>
@@ -303,7 +303,7 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"model2"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'model2'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 10 (100%) fits had some steps rejected. Maximum number of rejections was 9.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 10 (100%) fits had some steps rejected. Maximum number of rejections was 6.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
@@ -335,7 +335,7 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/brms.html b/docs/articles/brms.html
index 0a667b3..bc3a71f 100644
--- a/docs/articles/brms.html
+++ b/docs/articles/brms.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>SBC for brms models</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/brms.Rmd" class="external-link"><code>vignettes/brms.Rmd</code></a></small>
       <div class="hidden name"><code>brms.Rmd</code></div>
@@ -309,12 +309,15 @@ <h2 id="using-custom-generator-code">Using custom generator code<a class="anchor
 <span></span>
 <span><span class="va">n_sims_generator</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/SBC_generator_function.html">SBC_generator_function</a></span><span class="op">(</span><span class="va">one_sim_generator</span>, N <span class="op">=</span> <span class="fl">18</span>, K <span class="op">=</span> <span class="fl">5</span><span class="op">)</span></span></code></pre></div>
 <p>For increased sensitivity, we also add the log likelihood of the data
-given parameters as a generated quantity that we’ll also monitor (see
-the <a href="https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html"><code>limits_of_SBC</code></a>
+given parameters as a derived quantity that we’ll also monitor (see the
+<a href="https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html"><code>limits_of_SBC</code></a>
 vignette for discussion on why this is useful).</p>
 <div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">log_lik_gq_func</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generated_quantities.html">generated_quantities</a></span><span class="op">(</span></span>
-<span>  log_lik <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">dnorm</a></span><span class="op">(</span><span class="va">y</span>, <span class="va">b_Intercept</span> <span class="op">+</span> <span class="va">x</span> <span class="op">*</span> <span class="va">b_x</span> <span class="op">+</span> <span class="va">r_group</span><span class="op">[</span><span class="va">group</span><span class="op">]</span>, <span class="va">sigma</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">log_lik_dq_func</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/derived_quantities.html">derived_quantities</a></span><span class="op">(</span></span>
+<span>  log_lik <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">dnorm</a></span><span class="op">(</span><span class="va">y</span>, <span class="va">b_Intercept</span> <span class="op">+</span> <span class="va">x</span> <span class="op">*</span> <span class="va">b_x</span> <span class="op">+</span> <span class="va">r_group</span><span class="op">[</span><span class="va">group</span><span class="op">]</span>, <span class="va">sigma</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span>
+<span>  <span class="co"># Testing CRPS, probably not worth it</span></span>
+<span>  <span class="co">#, CRPS = mean(scoringRules::crps_norm(y, b_Intercept + x * b_x + r_group[group], sigma))</span></span>
+<span>  <span class="op">)</span></span></code></pre></div>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">12239755</span><span class="op">)</span></span>
 <span><span class="va">datasets_func</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="va">n_sims_generator</span>, <span class="fl">100</span><span class="op">)</span></span></code></pre></div>
@@ -335,7 +338,7 @@ <h2 id="using-custom-generator-code">Using custom generator code<a class="anchor
 <p>So we can happily compute:</p>
 <div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_func</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_func</span>, <span class="va">backend_func</span>, </span>
-<span>                                gen_quants <span class="op">=</span> <span class="va">log_lik_gq_func</span>, </span>
+<span>                                dquants <span class="op">=</span> <span class="va">log_lik_dq_func</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"func"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'func'</span></span></code></pre>
@@ -386,7 +389,7 @@ <h2 id="using-custom-generator-code">Using custom generator code<a class="anchor
 <p>Let’s fit the same simulations with the new backend.</p>
 <div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_func2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_func</span>, <span class="va">backend_func2</span>, </span>
-<span>                                 gen_quants <span class="op">=</span> <span class="va">log_lik_gq_func</span>, </span>
+<span>                                 dquants <span class="op">=</span> <span class="va">log_lik_dq_func</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"func2"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'func2'</span></span></code></pre>
@@ -428,7 +431,7 @@ <h2 id="using-custom-generator-code">Using custom generator code<a class="anchor
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/computational_algorithm1.html b/docs/articles/computational_algorithm1.html
index 6ac4209..8361cd5 100644
--- a/docs/articles/computational_algorithm1.html
+++ b/docs/articles/computational_algorithm1.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>SBC for ADVI and optimizing in Stan (+HMMs)</h1>
                         <h4 data-toc-skip class="author">Hyunji Moon,
 Martin Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/computational_algorithm1.Rmd" class="external-link"><code>vignettes/computational_algorithm1.Rmd</code></a></small>
       <div class="hidden name"><code>computational_algorithm1.Rmd</code></div>
@@ -288,8 +288,8 @@ <h2 id="example-i---poisson">Example I - Poisson<a class="anchor" aria-label="an
 <span><span class="co">##   variable width width_represented ci_low estimate ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>             <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>  <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">1</span> lambda    0.5               0.5   0.418    0.449   0.480</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">2</span> lambda    0.8               0.8   0.751    0.778   0.803</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">3</span> lambda    0.95              0.95  0.934    0.949   0.961</span></span></code></pre>
+<span><span class="co">## <span style="color: #BCBCBC;">2</span> lambda    0.8               0.8   0.752    0.779   0.804</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">3</span> lambda    0.95              0.95  0.932    0.948   0.960</span></span></code></pre>
 <div class="section level3">
 <h3 id="is-more-data-better">Is more data better?<a class="anchor" aria-label="anchor" href="#is-more-data-better"></a>
 </h3>
@@ -319,7 +319,7 @@ <h3 id="is-more-data-better">Is more data better?<a class="anchor" aria-label="a
 <pre><code><span><span class="co">## <span style="color: #949494;"># A tibble: 3 × 6</span></span></span>
 <span><span class="co">##   variable width width_represented ci_low estimate ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>             <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>  <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">1</span> lambda    0.5               0.5   0.412    0.443   0.474</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">1</span> lambda    0.5               0.5   0.414    0.445   0.476</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">2</span> lambda    0.8               0.8   0.682    0.711   0.738</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">3</span> lambda    0.95              0.95  0.883    0.903   0.920</span></span></code></pre>
 </div>
@@ -566,14 +566,14 @@ <h3 id="default-advi">Default ADVI<a class="anchor" aria-label="anchor" href="#d
 <pre><code><span><span class="co">## <span style="color: #949494;"># A tibble: 8 × 3</span></span></span>
 <span><span class="co">##   variable      ci_low ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>          <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">1</span> mu_background  0.820   0.882</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.746   0.818</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">3</span> rho[1]         0.864   0.918</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">4</span> rho[2]         0.864   0.918</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">5</span> t1[1]          0.805   0.869</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">6</span> t1[2]          0.805   0.869</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">7</span> t2[1]          0.831   0.891</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">8</span> t2[2]          0.831   0.891</span></span></code></pre>
+<span><span class="co">## <span style="color: #BCBCBC;">1</span> mu_background  0.818   0.880</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.752   0.823</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">3</span> rho[1]         0.860   0.914</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">4</span> rho[2]         0.860   0.914</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">5</span> t1[1]          0.814   0.877</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">6</span> t1[2]          0.814   0.877</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">7</span> t2[1]          0.835   0.895</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">8</span> t2[2]          0.835   0.895</span></span></code></pre>
 <p>So the 90% central credible interval for <code>mu_signal</code>
 likely contains less than 82% of true values.</p>
 <p>For a crude result, the default ADVI setup we just tested is not
@@ -630,13 +630,13 @@ <h3 id="full-rank">Full-rank<a class="anchor" aria-label="anchor" href="#full-ra
 <span><span class="co">##   variable      ci_low ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>          <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">1</span> mu_background  0.849   0.906</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.888   0.937</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">3</span> rho[1]         0.875   0.927</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">4</span> rho[2]         0.875   0.927</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.893   0.941</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">3</span> rho[1]         0.873   0.925</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">4</span> rho[2]         0.873   0.925</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">5</span> t1[1]          0.866   0.920</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">6</span> t1[2]          0.866   0.920</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">7</span> t2[1]          0.879   0.930</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">8</span> t2[2]          0.879   0.930</span></span></code></pre>
+<span><span class="co">## <span style="color: #BCBCBC;">7</span> t2[1]          0.877   0.929</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">8</span> t2[2]          0.877   0.929</span></span></code></pre>
 <p>This pattern where the default meanfield approximation is
 overconfident and the fullrank approximation is underconfident is in
 fact quite frequently seen, which motivated some experiments with a low
@@ -692,11 +692,11 @@ <h3 id="meanfield-lower-tolerance">Meanfield + lower tolerance<a class="anchor"
 <span><span class="co">##   variable      ci_low ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>          <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">1</span> mu_background  0.827   0.888</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.833   0.893</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu_signal      0.835   0.895</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">3</span> rho[1]         0.879   0.930</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">4</span> rho[2]         0.879   0.930</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">5</span> t1[1]          0.816   0.879</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">6</span> t1[2]          0.816   0.879</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">5</span> t1[1]          0.814   0.877</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">6</span> t1[2]          0.814   0.877</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">7</span> t2[1]          0.844   0.902</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;">8</span> t2[2]          0.844   0.902</span></span></code></pre>
 <p>This variant has somewhat lower overall mismatch, but tends to be
@@ -752,27 +752,22 @@ <h3 id="summary-2">Summary<a class="anchor" aria-label="anchor" href="#summary-2
 <span>  keep_fits <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>  cache_mode <span class="op">=</span> <span class="st">"results"</span>, cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"hmm_sample"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'hmm_sample'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 1 (2%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.019.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 1 (2%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
-<span><span class="co">## the rank statistics. The lowest tail ESS was 154.</span></span>
-<span><span class="co">##  If the fits look good otherwise, increasing `thin_ranks` (via recompute_SBC_statistics) </span></span>
-<span><span class="co">## or number of posterior draws (by refitting) might help.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 1 (2%) fits had divergent transitions. Maximum number of divergences was 51.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 2 (4%) fits had divergent transitions. Maximum number of divergences was 70.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>We get a small number of problematic fits, which we will ignore for
 now. We check that there are no obvious calibration problems:</p>
-<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb71"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_hmm_sample</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_sample_ecdf_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb72"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_hmm_sample</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_sample_ecdf_ranks-2.png" width="700"></p>
 <p>For the machine we built the vignette on, here are the distributions
 of times (for ADVI and optimizing) and time of longest chain (for
 HMC):</p>
-<div class="sourceCode" id="cb75"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb73"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">hmm_time</span> <span class="op">&lt;-</span> </span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/cbind.html" class="external-link">rbind</a></span><span class="op">(</span></span>
 <span>      <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>alg <span class="op">=</span> <span class="st">"Optimizing"</span>, </span>
@@ -807,7 +802,7 @@ <h3 id="summary-2">Summary<a class="anchor" aria-label="anchor" href="#summary-2
 model. However, both the fullrank and meanfield approximations provide
 not-terrible estimates and are noticeably faster than sampling.
 Optimizing is by far the fastest as the longest time observed is just
-0.17 seconds.</p>
+0.16 seconds.</p>
 </div>
 </div>
 <div class="section level2">
@@ -820,7 +815,7 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 difference between the two states) and move to the log scale. So instead
 of <code>mu_background</code> and <code>mu_signal</code> we have an
 <code>ordered</code> vector <code>log_mu</code>:</p>
-<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb74"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/readLines.html" class="external-link">readLines</a></span><span class="op">(</span><span class="st">"stan/hmm_poisson_ordered.stan"</span><span class="op">)</span>, sep <span class="op">=</span> <span class="st">"\n"</span><span class="op">)</span></span></code></pre></div>
 <pre><code>data {
   int N; // Number of observations
@@ -875,7 +870,7 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 that it implies a slightly different prior on the active (higher mean)
 state. Here is how we can generate data with this mildly different prior
 (we need rejection sampling to fulfill the ordering constraint):</p>
-<div class="sourceCode" id="cb78"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb76"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">generator_HMM_ordered</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">N</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  </span>
 <span>  <span class="co"># Rejection sampling for ordered mu with the correct priors</span></span>
@@ -922,10 +917,10 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 <span><span class="op">}</span></span></code></pre></div>
 <p>So let us build a default variational backend and fit it to just 20
 simulations.</p>
-<div class="sourceCode" id="cb79"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb77"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">model_HMM_ordered</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://mc-stan.org/cmdstanr/reference/cmdstan_model.html" class="external-link">cmdstan_model</a></span><span class="op">(</span><span class="st">"stan/hmm_poisson_ordered.stan"</span><span class="op">)</span></span>
 <span><span class="va">backend_HMM_ordered</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/SBC_backend_cmdstan_variational.html">SBC_backend_cmdstan_variational</a></span><span class="op">(</span><span class="va">model_HMM_ordered</span>, n_retries_init <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span></code></pre></div>
-<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb78"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">12333654</span><span class="op">)</span></span>
 <span><span class="va">ds_hmm_ordered</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span></span>
 <span>  <span class="fu"><a href="../reference/SBC_generator_function.html">SBC_generator_function</a></span><span class="op">(</span><span class="va">generator_HMM_ordered</span>, N <span class="op">=</span> <span class="fl">100</span><span class="op">)</span>, </span>
@@ -937,10 +932,10 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 <pre><code><span><span class="co">## Results loaded from cache file 'hmm_ordered'</span></span></code></pre>
 <p>Immediately we see that the <code>log_mu[1]</code> variable is
 heavily miscalibrated.</p>
-<div class="sourceCode" id="cb82"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb80"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_hmm_ordered</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_ecdf_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb83"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb81"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_hmm_ordered</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_ecdf_ranks-2.png" width="700"></p>
 <p>What changed? To understand that we need to remember how Stan <a href="https://mc-stan.org/docs/2_28/reference-manual/variable-transforms.html" class="external-link">represents
@@ -956,7 +951,7 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 complex correlation structure between the unconstrained parameters that
 the ADVI algorithm is unable to handle well.</p>
 <p>Even trying the fullrank variant does not help:</p>
-<div class="sourceCode" id="cb84"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb82"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">backend_HMM_ordered_fullrank</span> <span class="op">&lt;-</span> </span>
 <span>  <span class="fu"><a href="../reference/SBC_backend_cmdstan_variational.html">SBC_backend_cmdstan_variational</a></span><span class="op">(</span><span class="va">model_HMM_ordered</span>,</span>
 <span>                                  algorithm <span class="op">=</span> <span class="st">"fullrank"</span>, n_retries_init <span class="op">=</span> <span class="fl">3</span><span class="op">)</span></span>
@@ -966,14 +961,14 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 <span>                  cache_mode <span class="op">=</span> <span class="st">"results"</span>, cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"hmm_ordered_fullrank"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'hmm_ordered_fullrank'</span></span></code></pre>
 <p>The results are still strongly miscalibrated.</p>
-<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb84"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_hmm_ordered_fullrank</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_fullrank_ecdf_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb87"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb85"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_hmm_ordered_fullrank</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_fullrank_ecdf_ranks-2.png" width="700"></p>
 <p>To have a complete overview we may also try the optimizing fit:</p>
-<div class="sourceCode" id="cb88"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb86"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">model_HMM_ordered_rstan</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://mc-stan.org/rstan/reference/stan_model.html" class="external-link">stan_model</a></span><span class="op">(</span><span class="st">"stan/hmm_poisson_ordered.stan"</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">res_hmm_ordered_optimizing</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span></span>
@@ -984,10 +979,10 @@ <h2 id="example-iii---hidden-markov-model-ordered-variant">Example III - Hidden
 <p>in this case, optimizing has better calibration for
 <code>log_mu</code>, but worse calibration for <code>rho</code> than
 ADVI.</p>
-<div class="sourceCode" id="cb90"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb88"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_hmm_ordered_optimizing</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_optimizing_ecdf_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb91"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb89"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_hmm_ordered_optimizing</span><span class="op">)</span></span></code></pre></div>
 <p><img src="computational_algorithm1_files/figure-html/hmm_ordered_optimizing_ecdf_ranks-2.png" width="700"></p>
 </div>
@@ -1048,7 +1043,7 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
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diff --git a/docs/articles/discrete_vars.html b/docs/articles/discrete_vars.html
index d242305..abf75de 100644
--- a/docs/articles/discrete_vars.html
+++ b/docs/articles/discrete_vars.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -128,7 +128,7 @@ <h1 data-toc-skip>SBC with discrete parameters in Stan and
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/discrete_vars.Rmd" class="external-link"><code>vignettes/discrete_vars.Rmd</code></a></small>
       <div class="hidden name"><code>discrete_vars.Rmd</code></div>
@@ -256,24 +256,24 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <div class="sourceCode" id="cb6"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">85394672</span><span class="op">)</span></span>
 <span><span class="va">datasets_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="va">generator_1</span>, <span class="fl">30</span><span class="op">)</span></span></code></pre></div>
-<p>Additionally, we’ll add a generated quantity expressing the total
+<p>Additionally, we’ll add a derived quantity expressing the total
 log-likelihood of data given the fitted parameters. The expression
-within the <code><a href="../reference/generated_quantities.html">generated_quantities()</a></code> call is evaluated for
-both prior and posterior draws and included as another variable in SBC
-checks. It turns out this type of generated quantities can increase the
+within the <code><a href="../reference/derived_quantities.html">derived_quantities()</a></code> call is evaluated for both
+prior and posterior draws and included as another variable in SBC
+checks. It turns out this type of derived quantities can increase the
 sensitivity of the SBC against some issues in the model. See
 <code><a href="../articles/limits_of_SBC.html">vignette("limits_of_SBC")</a></code> for a more detailed discussion of
 this.</p>
 <div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">log_lik_gq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generated_quantities.html">generated_quantities</a></span><span class="op">(</span>log_lik <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Poisson.html" class="external-link">dpois</a></span><span class="op">(</span><span class="va">y</span>, <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="cn">T</span> <span class="op">&lt;</span> <span class="va">s</span>, <span class="va">e</span>, <span class="va">l</span><span class="op">)</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="va">log_lik_dq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/derived_quantities.html">derived_quantities</a></span><span class="op">(</span>log_lik <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Poisson.html" class="external-link">dpois</a></span><span class="op">(</span><span class="va">y</span>, <span class="fu"><a href="https://rdrr.io/r/base/ifelse.html" class="external-link">ifelse</a></span><span class="op">(</span><span class="fl">1</span><span class="op">:</span><span class="cn">T</span> <span class="op">&lt;</span> <span class="va">s</span>, <span class="va">e</span>, <span class="va">l</span><span class="op">)</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <p>So finally, lets actually compute SBC:</p>
 <div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_1</span>, <span class="va">backend_1</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"model1"</span><span class="op">)</span>,</span>
-<span>                    gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span><span class="op">)</span></span></code></pre></div>
+<span>                    dquants <span class="op">=</span> <span class="va">log_lik_dq</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'model1'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 5 (17%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 4 (13%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
 <pre><code><span><span class="co">##  - 20 (67%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
 <span><span class="co">## the rank statistics. The lowest tail ESS was NA.</span></span>
 <span><span class="co">##  If the fits look good otherwise, increasing `thin_ranks` (via recompute_SBC_statistics) </span></span>
@@ -297,12 +297,12 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <pre><code><span><span class="co">## <span style="color: #949494;"># A tibble: 30 × 15</span></span></span>
 <span><span class="co">##    sim_id variable simulated_value  rank   z_score  mean median    sd   mad</span></span>
 <span><span class="co">##     <span style="color: #949494; font-style: italic;">&lt;int&gt;</span> <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>              <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>     <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>  <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span> <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">## <span style="color: #BCBCBC;"> 1</span>      1 s                      3   185    0.018<span style="text-decoration: underline;">2</span>  2.97      3 1.61   2.97</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;"> 1</span>      1 s                      3   186    0.020<span style="text-decoration: underline;">0</span>  2.97      3 1.59   2.97</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 2</span>      2 s                      1    24   -<span style="color: #BB0000;">1.90</span>    2.02      2 0.537  0   </span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 3</span>      3 s                      4   126   -<span style="color: #BB0000;">1.37</span>    4.67      5 0.489  0   </span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 4</span>      4 s                      1    10   -<span style="color: #BB0000;">2.85</span>    2.86      3 0.651  0   </span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 5</span>      5 s                      5   397    2.76    2.86      3 0.775  0   </span></span>
-<span><span class="co">## <span style="color: #BCBCBC;"> 6</span>      6 s                      2   271    0.044<span style="text-decoration: underline;">9</span>  1.94      1 1.42   0   </span></span>
+<span><span class="co">## <span style="color: #BCBCBC;"> 6</span>      6 s                      2   290    0.118   1.84      1 1.35   0   </span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 7</span>      7 s                      3     0 -<span style="color: #BB0000;">Inf</span>       4         4 0      0   </span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 8</span>      8 s                      2   129   -<span style="color: #BB0000;">0.594</span>   2.87      3 1.46   1.48</span></span>
 <span><span class="co">## <span style="color: #BCBCBC;"> 9</span>      9 s                      2     0   -<span style="color: #BB0000;">6.84</span>    2.99      3 0.144  0   </span></span>
@@ -315,7 +315,7 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <p>Looking at the <code>ecdf_diff</code> plot we see that this seems to
 compromise heavily the inference for <code>s</code>, but the other
 parameters do not show such bad behaviour. Note that the
-<code>log_lik</code> generated quantity shows even starker failure than
+<code>log_lik</code> derived quantity shows even starker failure than
 <code>s</code>, so it indeed poses a stricter check in this
 scenario.</p>
 <div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
@@ -376,7 +376,7 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">5846502</span><span class="op">)</span></span>
 <span><span class="va">datasets_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="va">generator_2</span>, <span class="fl">30</span><span class="op">)</span></span>
 <span><span class="va">results_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_2</span>, <span class="va">backend_1</span>,</span>
-<span>                    gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span>, </span>
+<span>                    dquants <span class="op">=</span> <span class="va">log_lik_dq</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"model2"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'model2'</span></span></code></pre>
@@ -401,16 +401,16 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">54321488</span><span class="op">)</span></span>
 <span><span class="va">datasets_2_more</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="va">generator_2</span>, <span class="fl">100</span><span class="op">)</span></span>
 <span><span class="va">results_2_more</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_2_more</span>, <span class="va">backend_1</span>,</span>
-<span>                    gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span>, </span>
+<span>                    dquants <span class="op">=</span> <span class="va">log_lik_dq</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"model3"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'model3'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 15 (15%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 73 (73%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
+<pre><code><span><span class="co">##  - 72 (72%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
 <span><span class="co">## the rank statistics. The lowest tail ESS was NA.</span></span>
 <span><span class="co">##  If the fits look good otherwise, increasing `thin_ranks` (via recompute_SBC_statistics) </span></span>
 <span><span class="co">## or number of posterior draws (by refitting) might help.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 7 (7%) fits had divergent transitions. Maximum number of divergences was 20.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 9 (9%) fits had divergent transitions. Maximum number of divergences was 25.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
@@ -424,7 +424,7 @@ <h2 id="stan-version-and-debugging">Stan version and debugging<a class="anchor"
 <p><img src="discrete_vars_files/figure-html/results_2_all_plots-2.png" width="700"></p>
 <p>Now - as far as this amount of SBC steps can see, the model is good
 and we get good behaviour for both the continuous and the discrete
-parameters and the <code>log_lik</code> generated quantity. Hooray!</p>
+parameters and the <code>log_lik</code> derived quantity. Hooray!</p>
 </div>
 <div class="section level2">
 <h2 id="jags-version">JAGS version<a class="anchor" aria-label="anchor" href="#jags-version"></a>
@@ -469,12 +469,12 @@ <h2 id="jags-version">JAGS version<a class="anchor" aria-label="anchor" href="#j
 <div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">datasets_2_all</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/bind_datasets.html">bind_datasets</a></span><span class="op">(</span><span class="va">datasets_2</span>, <span class="va">datasets_2_more</span><span class="op">)</span></span>
 <span><span class="va">results_jags</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_2_all</span>, <span class="va">backend_jags</span>,</span>
-<span>                            gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span>,</span>
+<span>                            dquants <span class="op">=</span> <span class="va">log_lik_dq</span>,</span>
 <span>                        cache_mode <span class="op">=</span> <span class="st">"results"</span>,</span>
 <span>                        cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir_jags</span>, <span class="st">"rjags"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'rjags'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 21 (16%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 95 (73%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
+<pre><code><span><span class="co">##  - 20 (15%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 93 (72%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
 <span><span class="co">## the rank statistics. The lowest tail ESS was NA.</span></span>
 <span><span class="co">##  If the fits look good otherwise, increasing `thin_ranks` (via recompute_SBC_statistics) </span></span>
 <span><span class="co">## or number of posterior draws (by refitting) might help.</span></span></code></pre>
@@ -550,12 +550,12 @@ <h2 id="jags-version">JAGS version<a class="anchor" aria-label="anchor" href="#j
 <p>Then we run the actual SBC:</p>
 <div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_jags_marginalized</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_2_all</span>, <span class="va">backend_jags_marginalized</span>,</span>
-<span>                                         gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span>,</span>
+<span>                                         dquants <span class="op">=</span> <span class="va">log_lik_dq</span>,</span>
 <span>                        cache_mode <span class="op">=</span> <span class="st">"results"</span>,</span>
 <span>                        cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir_jags</span>, <span class="st">"rjags_marginalized"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'rjags_marginalized'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 24 (18%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 89 (68%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
+<pre><code><span><span class="co">##  - 26 (20%) fits had at least one Rhat &gt; 1.01. Largest Rhat was NA.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 93 (72%) fits had tail ESS undefined or less than half of the maximum rank, potentially skewing </span></span>
 <span><span class="co">## the rank statistics. The lowest tail ESS was NA.</span></span>
 <span><span class="co">##  If the fits look good otherwise, increasing `thin_ranks` (via recompute_SBC_statistics) </span></span>
 <span><span class="co">## or number of posterior draws (by refitting) might help.</span></span></code></pre>
@@ -590,7 +590,7 @@ <h2 id="jags-version">JAGS version<a class="anchor" aria-label="anchor" href="#j
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
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index 38556e0..064d2e7 100644
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diff --git a/docs/articles/implementing_backends.html b/docs/articles/implementing_backends.html
index 3a705d3..c38216b 100644
--- a/docs/articles/implementing_backends.html
+++ b/docs/articles/implementing_backends.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -128,7 +128,7 @@ <h1 data-toc-skip>Implementing a new backend (algorithm) +
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/implementing_backends.Rmd" class="external-link"><code>vignettes/implementing_backends.Rmd</code></a></small>
       <div class="hidden name"><code>implementing_backends.Rmd</code></div>
@@ -275,13 +275,14 @@ <h2 id="minimal-backend-support">Minimal backend support<a class="anchor" aria-l
 <span>                               thin_ranks <span class="op">=</span> <span class="fl">1</span>,</span>
 <span>                               cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                               cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>,<span class="st">"poisson"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'poisson'</span></span></code></pre>
 <p>We have set <code>thin_ranks = 1</code> as no thinning is needed (the
 draws are i.i.d. by construction).</p>
 <p>The rank and ecdf plots show no big problems</p>
-<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_poisson</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/poisson_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_poisson</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/poisson_ranks-2.png" width="700"></p>
 <p>This is not unexpected - we’ve used a large number of observations
@@ -290,7 +291,7 @@ <h2 id="minimal-backend-support">Minimal backend support<a class="anchor" aria-l
 Bayesian solution.</p>
 <p>We can see that both variables are recovered almost exactly in almost
 all fits:</p>
-<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">res_poisson</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/poisson_sim_estimated-1.png" width="700"></p>
 </div>
@@ -307,7 +308,7 @@ <h2 id="additional-backend-improvements">Additional backend improvements<a class
 package will then by default use <code>thin_ranks = 1</code> argument to
 <code>compute_SBC</code> and will not assess convergence/autocorrelation
 via the R-hat and ESS diagnostics.</p>
-<div class="sourceCode" id="cb10"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">SBC_backend_iid_draws.SBC_backend_glm</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">backend</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="cn">TRUE</span></span>
 <span><span class="op">}</span></span></code></pre></div>
@@ -318,7 +319,7 @@ <h2 id="additional-backend-improvements">Additional backend improvements<a class
 understand whether there was some problem in fitting.</p>
 <p>To see some of the problems that <code>glm</code> can encounter,
 we’ll run a quite pathological logistic regression:</p>
-<div class="sourceCode" id="cb11"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">problematic_data</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span>y <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/rep.html" class="external-link">rep</a></span><span class="op">(</span><span class="fl">0</span><span class="op">:</span><span class="fl">1</span>, each <span class="op">=</span> <span class="fl">100</span><span class="op">)</span>, x <span class="op">=</span> <span class="fl">1</span><span class="op">:</span><span class="fl">200</span><span class="op">)</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/stats/glm.html" class="external-link">glm</a></span><span class="op">(</span><span class="va">y</span> <span class="op">~</span> <span class="va">x</span>, data <span class="op">=</span> <span class="va">problematic_data</span>, family <span class="op">=</span> <span class="st">"binomial"</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Warning: glm.fit: algorithm did not converge</span></span></code></pre>
@@ -348,7 +349,7 @@ <h2 id="additional-backend-improvements">Additional backend improvements<a class
 is often useful to add a custom class to the results to allow for
 automatic summaries (we’ll get there). This is our implementation for
 the <code>glm</code> class:</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">SBC_fit_to_diagnostics.glm</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">fit</span>, <span class="va">fit_output</span>, <span class="va">fit_messages</span>, <span class="va">fit_warnings</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="va">res</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/data.frame.html" class="external-link">data.frame</a></span><span class="op">(</span></span>
 <span>    probs_0_1 <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/any.html" class="external-link">any</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/grep.html" class="external-link">grepl</a></span><span class="op">(</span><span class="st">"fitted probabilities numerically 0 or 1 occurred"</span>, <span class="va">fit_warnings</span><span class="op">)</span><span class="op">)</span>,</span>
@@ -360,7 +361,7 @@ <h2 id="additional-backend-improvements">Additional backend improvements<a class
 <span><span class="op">}</span></span></code></pre></div>
 <p>Having a custom class let’s us implement a <code>summary</code>
 implementation for our diagnostics:</p>
-<div class="sourceCode" id="cb16"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">summary.SBC_glm_diagnostics</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="va">summ</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span></span>
 <span>    n_fits <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/nrow.html" class="external-link">nrow</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span>,</span>
@@ -378,7 +379,7 @@ <h2 id="additional-backend-improvements">Additional backend improvements<a class
 <code>SBC_results</code> object.</p>
 <p>We’ll use our <code>summary</code> implementation for
 <code>SBC_glm_diagnostics</code> to create the messages:</p>
-<div class="sourceCode" id="cb17"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">get_diagnostic_messages.SBC_glm_diagnostics</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">x</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="../reference/get_diagnostic_messages.html">get_diagnostic_messages</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/summary.html" class="external-link">summary</a></span><span class="op">(</span><span class="va">x</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span></span>
@@ -479,7 +480,7 @@ <h2 id="glm-as-approximate-bayesian-method">
 normal priors on the intercept and predictors. Note that we do some <a href="https://hyunjimoon.github.io/SBC/articles/rejection_sampling.html">rejection
 sampling</a> here to avoid using simulations where the generated
 response is the same or almost the same for all rows.</p>
-<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">generator_single_logistic</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">formula</span>, </span>
 <span>                                      <span class="va">template_data</span>, </span>
 <span>                                      <span class="va">intercept_prior_loc</span> <span class="op">=</span> <span class="fl">0</span>,</span>
@@ -532,7 +533,7 @@ <h3 id="well-informed-model">Well-informed model<a class="anchor" aria-label="an
 <p>We’ll start by testing our approximate computation with the simplest
 analysis - the primary binary outcome predicted only by the treatment
 (the <code>rx</code> column in the data):</p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">formula_indo_simple</span> <span class="op">&lt;-</span> <span class="va">outcome</span> <span class="op">~</span> <span class="va">rx</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">6524243</span><span class="op">)</span></span>
 <span><span class="va">datasets_indo_simple</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="fu"><a href="../reference/SBC_generator_function.html">SBC_generator_function</a></span><span class="op">(</span></span>
@@ -542,24 +543,25 @@ <h3 id="well-informed-model">Well-informed model<a class="anchor" aria-label="an
 <span>  n_sims <span class="op">=</span> <span class="fl">500</span><span class="op">)</span> </span>
 <span></span>
 <span><span class="va">backend_indo_simple</span> <span class="op">&lt;-</span> <span class="fu">SBC_backend_glm</span><span class="op">(</span>formula <span class="op">=</span> <span class="va">formula_indo_simple</span>, family <span class="op">=</span> <span class="st">"binomial"</span><span class="op">)</span> </span></code></pre></div>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res_indo_simple</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_indo_simple</span>, <span class="va">backend_indo_simple</span>,</span>
 <span>                                   cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                                   cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>,<span class="st">"indo_simple"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'indo_simple'</span></span></code></pre>
 <p>The rank plots look good:</p>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_indo_simple</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_indo_simple</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_ranks-2.png" width="700"></p>
 <p>The coverages are very tight</p>
-<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_coverage.html">plot_coverage</a></span><span class="op">(</span><span class="va">res_indo_simple</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_sim_coverage-1.png" width="700"></p>
 <p>we can make this precise by inspecting the same results
 numerically:</p>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">stats_effect</span> <span class="op">&lt;-</span> <span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">[</span><span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">$</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"rx1_indomethacin"</span>,<span class="op">]</span></span>
 <span><span class="va">main_eff_coverage</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/empirical_coverage.html">empirical_coverage</a></span><span class="op">(</span><span class="va">stats_effect</span>, width <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>,<span class="fl">0.9</span>, <span class="fl">0.95</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">main_eff_coverage</span></span></code></pre></div>
@@ -575,13 +577,13 @@ <h3 id="well-informed-model">Well-informed model<a class="anchor" aria-label="an
 we are happy that there clearly is no substantial discrepancy.</p>
 <p>We may want to also look at how tight estimates we get - looking
 directly gives us a somewhat unhelpful plot:</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">res_indo_simple</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_sim_est_ugly-1.png" width="700"></p>
 <p>There is a simulation where the posterior uncertainty is very large.
 This corresponds to observed data where the outcome is the same for all
 rows where the treatment was used:</p>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">biggest_sd_sim</span> <span class="op">&lt;-</span> <span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">$</span><span class="va">sim_id</span><span class="op">[</span></span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/which.min.html" class="external-link">which.max</a></span><span class="op">(</span><span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">$</span><span class="va">sd</span><span class="op">)</span><span class="op">]</span></span>
 <span><span class="fu"><a href="https://rdrr.io/r/base/table.html" class="external-link">table</a></span><span class="op">(</span><span class="va">datasets_indo_simple</span><span class="op">$</span><span class="va">generated</span><span class="op">[[</span><span class="va">biggest_sd_sim</span><span class="op">]</span><span class="op">]</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"outcome"</span>, <span class="st">"rx"</span><span class="op">)</span><span class="op">]</span><span class="op">)</span></span></code></pre></div>
@@ -591,7 +593,7 @@ <h3 id="well-informed-model">Well-informed model<a class="anchor" aria-label="an
 <span><span class="co">##       1       281            295</span></span></code></pre>
 <p>Filtering the extreme simulations out, we see that most commonly, we
 get a decently precise estimate.</p>
-<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">stats_filtered</span> <span class="op">&lt;-</span> <span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">[</span><span class="va">res_indo_simple</span><span class="op">$</span><span class="va">stats</span><span class="op">$</span><span class="va">sd</span> <span class="op">&lt;</span> <span class="fl">200</span>, <span class="op">]</span></span>
 <span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">stats_filtered</span>, alpha <span class="op">=</span> <span class="fl">0.3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_sim_est-1.png" width="700"></p>
@@ -608,7 +610,7 @@ <h3 id="badly-informed-model">Badly-informed model<a class="anchor" aria-label="
 <span class="math inline">\(N(0,1)\)</span> prior on the age coefficient
 have a sensible scale. To make matters worse, we further subsample the
 data to contain only 100 rows.</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">21645222</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">indo_rct_complex</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/droplevels.html" class="external-link">droplevels</a></span><span class="op">(</span></span>
@@ -628,10 +630,11 @@ <h3 id="badly-informed-model">Badly-informed model<a class="anchor" aria-label="
 <span></span>
 <span><span class="va">backend_indo_complex</span> <span class="op">&lt;-</span> <span class="fu">SBC_backend_glm</span><span class="op">(</span>formula <span class="op">=</span> <span class="va">formula_indo_complex</span>, family <span class="op">=</span> <span class="st">"binomial"</span><span class="op">)</span> </span></code></pre></div>
 <p>Now we are ready to run SBC:</p>
-<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res_indo_complex</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_indo_complex</span>, <span class="va">backend_indo_complex</span>,</span>
 <span>                                   cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                                   cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>,<span class="st">"indo_complex"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'indo_complex'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 19 (4%) of fits had 0/1 probabilities.</span></span></code></pre>
 <pre><code><span><span class="co">##  - 2 (0%) of fits did not converge.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
@@ -641,10 +644,10 @@ <h3 id="badly-informed-model">Badly-informed model<a class="anchor" aria-label="
 are notified of some problems.</p>
 <p>Additionally the rank plots shows some miscalibration, most
 pronounced for the <code>site3_UK</code> coefficients:</p>
-<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb39"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_indo_complex</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_complex_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_indo_complex</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_complex_ranks-2.png" width="700"></p>
 <p>What happens is that many of the simulations result in extremely wide
@@ -654,7 +657,7 @@ <h3 id="badly-informed-model">Badly-informed model<a class="anchor" aria-label="
 would regularize the uncertainties and avoid this problem.</p>
 <p>The main effect of interest (<code>rx1_indomethacin</code>) is
 however still reasonably well calibrated</p>
-<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">stats_effect</span> <span class="op">&lt;-</span> <span class="va">res_indo_complex</span><span class="op">$</span><span class="va">stats</span><span class="op">[</span><span class="va">res_indo_complex</span><span class="op">$</span><span class="va">stats</span><span class="op">$</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"rx1_indomethacin"</span>,<span class="op">]</span></span>
 <span><span class="va">main_eff_coverage</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/empirical_coverage.html">empirical_coverage</a></span><span class="op">(</span><span class="va">stats_effect</span>, width <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>,<span class="fl">0.9</span>, <span class="fl">0.95</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">main_eff_coverage</span></span></code></pre></div>
@@ -672,7 +675,7 @@ <h3 id="badly-informed-model-narrow-priors">Badly-informed model, narrow priors<
 posterior problematic. We can obviously make things worse by also
 introducing a strong prior, concentrating away from zero which we’ll do
 here:</p>
-<div class="sourceCode" id="cb40"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">1685554</span><span class="op">)</span></span>
 <span><span class="va">datasets_indo_complex_narrow</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="fu"><a href="../reference/SBC_generator_function.html">SBC_generator_function</a></span><span class="op">(</span></span>
 <span>  <span class="va">generator_single_logistic</span>, </span>
@@ -683,10 +686,11 @@ <h3 id="badly-informed-model-narrow-priors">Badly-informed model, narrow priors<
 <span>  predictor_prior_loc <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span><span class="op">)</span>,</span>
 <span>  predictor_prior_width <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span>,</span>
 <span>  n_sims <span class="op">=</span> <span class="fl">500</span><span class="op">)</span> </span></code></pre></div>
-<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res_indo_complex_narrow</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_indo_complex_narrow</span>, <span class="va">backend_indo_complex</span>,</span>
 <span>                                   cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                                   cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>,<span class="st">"indo_complex_narrow"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'indo_complex_narrow'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 169 (34%) of fits had 0/1 probabilities.</span></span></code></pre>
 <pre><code><span><span class="co">##  - 2 (0%) of fits did not converge.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
@@ -694,10 +698,10 @@ <h3 id="badly-informed-model-narrow-priors">Badly-informed model, narrow priors<
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>This is enough to make basically all the variables poorly
 calibrated:</p>
-<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_indo_complex_narrow</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_complex_narrow_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_indo_complex_narrow</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_complex_narrow_ranks-2.png" width="700"></p>
 </div>
@@ -706,7 +710,7 @@ <h3 id="well-informed-model-narrow-priors">Well-informed model, narrow priors<a
 </h3>
 <p>To make the analysis complete, we’ll also return to the simple,
 well-informed model, but use narrow priors.</p>
-<div class="sourceCode" id="cb47"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">3289542</span><span class="op">)</span></span>
 <span><span class="va">datasets_indo_simple_narrow</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="fu"><a href="../reference/SBC_generator_function.html">SBC_generator_function</a></span><span class="op">(</span></span>
 <span>  <span class="va">generator_single_logistic</span>, </span>
@@ -717,17 +721,18 @@ <h3 id="well-informed-model-narrow-priors">Well-informed model, narrow priors<a
 <span>  predictor_prior_loc <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="op">-</span><span class="fl">2</span>, <span class="fl">2</span><span class="op">)</span>,</span>
 <span>  predictor_prior_width <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span>,</span>
 <span>  n_sims <span class="op">=</span> <span class="fl">500</span><span class="op">)</span> </span></code></pre></div>
-<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">res_indo_simple_narrow</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_indo_simple_narrow</span>, <span class="va">backend_indo_simple</span>,</span>
 <span>                                   cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                                   cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>,<span class="st">"indo_simple_narrow"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'indo_simple_narrow'</span></span></code></pre>
 <p>Turns out that in this case, the likelihood is sometimes not enough
 to completely overwhelm the prior and the main treatment effect is
 poorly calibrated:</p>
-<div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_indo_simple_narrow</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_narrow_ranks-1.png" width="700"></p>
-<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb55"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_indo_simple_narrow</span><span class="op">)</span></span></code></pre></div>
 <p><img src="implementing_backends_files/figure-html/indo_simple_narrow_ranks-2.png" width="700"></p>
 </div>
@@ -763,7 +768,7 @@ <h2 id="conclusions">Conclusions<a class="anchor" aria-label="anchor" href="#con
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/index.html b/docs/articles/index.html
index 7eb0680..e32219f 100644
--- a/docs/articles/index.html
+++ b/docs/articles/index.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -147,7 +147,7 @@ <h3>Additional use cases and advanced topics</h3>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/articles/indexing.html b/docs/articles/indexing.html
index 5af0197..a9f9bb8 100644
--- a/docs/articles/indexing.html
+++ b/docs/articles/indexing.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Discovering indexing errors with SBC</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/indexing.Rmd" class="external-link"><code>vignettes/indexing.Rmd</code></a></small>
       <div class="hidden name"><code>indexing.Rmd</code></div>
@@ -301,43 +301,46 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 <code class="sourceCode R"><span><span class="va">results_regression_1</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_regression</span>, <span class="va">backend_regression_1</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"regression1"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'regression1'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 7 (70%) fits had some steps rejected. Maximum number of rejections was 4.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_regression_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_regression</span>, <span class="va">backend_regression_2</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"regression2"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'regression2'</span></span></code></pre>
 <pre><code><span><span class="co">##  - 1 (10%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.011.</span></span></code></pre>
 <pre><code><span><span class="co">##  - 6 (60%) fits had some steps rejected. Maximum number of rejections was 4.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
-<div class="sourceCode" id="cb18"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_regression_3</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_regression</span>, <span class="va">backend_regression_3</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"regression3"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">##  - 3 (30%) fits had some steps rejected. Maximum number of rejections was 3.</span></span>
-<span><span class="co">## Not all diagnostics are OK.</span></span>
+<pre><code><span><span class="co">## Results loaded from cache file 'regression3'</span></span></code></pre>
+<pre><code><span><span class="co">##  - 3 (30%) fits had some steps rejected. Maximum number of rejections was 3.</span></span></code></pre>
+<pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>Here we also use the caching feature to avoid recomputing the fits
 when recompiling this vignette. In practice, caching is not necessary
 but is often useful.</p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_regression_1</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression1-1.png" width="700"></p>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_regression_1</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression1-2.png" width="700"></p>
 <p>As far as a quick SBC can see the first code is OK. You could verify
 further with more iterations but we tested the model for you and it is
 OK (although the implementation is not the best one).</p>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_regression_2</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression2-1.png" width="700"></p>
-<div class="sourceCode" id="cb23"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_regression_2</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression2-2.png" width="700"></p>
 <p>But the second model is actually not looking good. In fact there is
@@ -347,10 +350,10 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 to the <code>sigma</code> variable (reusing the same <code>x</code>
 element leads to more similar predictions for each row, so
 <code>sigma</code> needs to be inflated to accommodate this)</p>
-<div class="sourceCode" id="cb24"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_regression_3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression3-1.png" width="700"></p>
-<div class="sourceCode" id="cb25"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_regression_3</span><span class="op">)</span></span></code></pre></div>
 <p><img src="indexing_files/figure-html/plots_regression3-2.png" width="700"></p>
 <p>And the third model looks OK once again - and in fact we are pretty
@@ -372,7 +375,7 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/limits_of_SBC.html b/docs/articles/limits_of_SBC.html
index 109514d..2ed4558 100644
--- a/docs/articles/limits_of_SBC.html
+++ b/docs/articles/limits_of_SBC.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Limits of SBC</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/limits_of_SBC.Rmd" class="external-link"><code>vignettes/limits_of_SBC.Rmd</code></a></small>
       <div class="hidden name"><code>limits_of_SBC.Rmd</code></div>
@@ -136,12 +136,16 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 
     
     
-<p>Here, we’ll walk through some problems that are hard/impossible to
-diagnose with SBC. As usual the focus is on problems with models,
-assuming our inference algorithm is correct. But for each of those
-problems, one can imagine a corresponding failure in an algorithm —
-although some of those failures are quite unlikely for actual
+<p>Here, we’ll walk through some problems that are hard to diagnose with
+SBC in its default settings. As usual the focus is on problems with
+models, assuming our inference algorithm is correct. But for each of
+those problems, one can imagine a corresponding failure in an algorithm
+— although some of those failures are quite unlikely for actual
 algorithms.</p>
+<p>A more extensive theoretical discussion of those limits can be found
+in the <a href="https://arxiv.org/abs/2211.02383v1" class="external-link">Simulation-Based
+Calibration Checking for Bayesian Computation: The Choice of Test
+Quantities Shapes Sensitivity</a> preprint, additional examples at <a href="https://martinmodrak.github.io/sbc_test_quantities_paper/" class="external-link uri">https://martinmodrak.github.io/sbc_test_quantities_paper/</a></p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://hyunjimoon.github.io/SBC/">SBC</a></span><span class="op">)</span></span>
 <span><span class="kw"><a href="https://rdrr.io/r/base/library.html" class="external-link">library</a></span><span class="op">(</span><span class="va"><a href="https://ggplot2.tidyverse.org" class="external-link">ggplot2</a></span><span class="op">)</span></span>
@@ -261,23 +265,22 @@ <h2 id="sbc-and-minor-changes-to-model">SBC and minor changes to model<a class="
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"minor_10"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'minor_10'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 1 (10%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.024.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 2 (20%) fits had some steps rejected. Maximum number of rejections was 1.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 3 (30%) fits had some steps rejected. Maximum number of rejections was 2.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>Not really…</p>
-<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb12"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_minor_10</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_10_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb13"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_minor_10</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_10_plots-2.png" width="700"></p>
 <p>Will we have better luck with 100 simulations? (Note that we can use
 <code>bind_results</code> to combine multiple results, letting us start
 small, but not throw away the computation spent for the initial
 simulations)</p>
-<div class="sourceCode" id="cb15"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb14"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_minor_100</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/bind_results.html">bind_results</a></span><span class="op">(</span></span>
 <span>  <span class="va">results_minor_10</span>,</span>
 <span>  <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_minor</span><span class="op">[</span><span class="fl">11</span><span class="op">:</span><span class="fl">100</span><span class="op">]</span>, <span class="va">backend_minor</span>, </span>
@@ -285,21 +288,21 @@ <h2 id="sbc-and-minor-changes-to-model">SBC and minor changes to model<a class="
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"minor_90"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'minor_90'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 6 (7%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.02.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 16 (18%) fits had some steps rejected. Maximum number of rejections was 1.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 7 (8%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.02.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 13 (14%) fits had some steps rejected. Maximum number of rejections was 1.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>Here we see something suspicios with the <code>sigma</code> variable,
 but it is not very convincing.</p>
-<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb19"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_minor_100</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_100_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb20"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_minor_100</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_100_plots-2.png" width="700"></p>
 <p>So let’s do additional 100 SBC steps</p>
-<div class="sourceCode" id="cb22"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb21"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_minor_200</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/bind_results.html">bind_results</a></span><span class="op">(</span></span>
 <span>  <span class="va">results_minor_100</span>,</span>
 <span>  <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_minor</span><span class="op">[</span><span class="fl">101</span><span class="op">:</span><span class="fl">200</span><span class="op">]</span>, <span class="va">backend_minor</span>, </span>
@@ -307,17 +310,17 @@ <h2 id="sbc-and-minor-changes-to-model">SBC and minor changes to model<a class="
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"minor_next_100"</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'minor_next_100'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 6 (6%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.02.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 14 (14%) fits had some steps rejected. Maximum number of rejections was 1.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 9 (9%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.016.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 12 (12%) fits had some steps rejected. Maximum number of rejections was 2.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>OK, so this looks at least a bit conclusive, but still, the violation
 of uniformity is not very big.</p>
-<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb26"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_minor_200</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_200_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb27"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_minor_200</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_200_plots-2.png" width="700"></p>
 <p>If we used more data points per simulation (here we simulated just
@@ -329,35 +332,35 @@ <h2 id="sbc-and-minor-changes-to-model">SBC and minor changes to model<a class="
 this is to plot the posterior mean + central 90% interval against the
 simulated value via <code>plot_sim_estimated</code>. The estimates
 should cluster around the y=x line (blue), which they mostly do.</p>
-<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb28"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">results_minor_200</span>, alpha <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_200_sim_estimated-1.png" width="700"></p>
 <p>Another way to investigate this is the coverage plot, showing the
 attained coverage of various central credible intervals.</p>
-<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb29"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_coverage.html">plot_coverage</a></span><span class="op">(</span><span class="va">results_minor_200</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_minor_200_coverage-1.png" width="700"></p>
 <p>Or we can even directly inspect some intervals of interest:</p>
-<div class="sourceCode" id="cb31"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb30"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">coverage</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/empirical_coverage.html">empirical_coverage</a></span><span class="op">(</span><span class="va">results_minor_200</span><span class="op">$</span><span class="va">stats</span>, width <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">0.5</span>,<span class="fl">0.9</span>,<span class="fl">0.95</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="va">coverage</span></span></code></pre></div>
 <pre><code><span><span class="co">## <span style="color: #949494;"># A tibble: 6 × 6</span></span></span>
 <span><span class="co">##   variable width width_represented ci_low estimate ci_high</span></span>
 <span><span class="co">##   <span style="color: #949494; font-style: italic;">&lt;chr&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>             <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>  <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>    <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span>   <span style="color: #949494; font-style: italic;">&lt;dbl&gt;</span></span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">1</span> mu        0.5               0.5   0.407    0.475   0.544</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu        0.9               0.9   0.862    0.91    0.942</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">3</span> mu        0.95              0.95  0.930    0.965   0.983</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">4</span> sigma     0.5               0.5   0.368    0.435   0.504</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">5</span> sigma     0.9               0.9   0.750    0.81    0.858</span></span>
-<span><span class="co">## <span style="color: #BCBCBC;">6</span> sigma     0.95              0.95  0.839    0.89    0.926</span></span></code></pre>
-<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
+<span><span class="co">## <span style="color: #BCBCBC;">1</span> mu        0.5               0.5   0.397    0.465   0.534</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">2</span> mu        0.9               0.9   0.856    0.905   0.938</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">3</span> mu        0.95              0.95  0.923    0.96    0.979</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">4</span> sigma     0.5               0.5   0.373    0.44    0.509</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">5</span> sigma     0.9               0.9   0.728    0.79    0.841</span></span>
+<span><span class="co">## <span style="color: #BCBCBC;">6</span> sigma     0.95              0.95  0.828    0.88    0.918</span></span></code></pre>
+<div class="sourceCode" id="cb32"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">sigma_90_coverage_string</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/paste.html" class="external-link">paste0</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/Round.html" class="external-link">round</a></span><span class="op">(</span><span class="fl">100</span> <span class="op">*</span> <span class="fu"><a href="https://rdrr.io/r/base/numeric.html" class="external-link">as.numeric</a></span><span class="op">(</span></span>
 <span>  <span class="va">coverage</span><span class="op">[</span><span class="va">coverage</span><span class="op">$</span><span class="va">variable</span> <span class="op">==</span> <span class="st">"sigma"</span> <span class="op">&amp;</span> <span class="va">coverage</span><span class="op">$</span><span class="va">width</span> <span class="op">==</span> <span class="fl">0.9</span>, <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"ci_low"</span>,<span class="st">"ci_high"</span><span class="op">)</span><span class="op">]</span><span class="op">)</span><span class="op">)</span>,</span>
 <span>  <span class="st">"%"</span>,</span>
 <span>  collapse <span class="op">=</span> <span class="st">" - "</span><span class="op">)</span></span></code></pre></div>
 <p>where we see that for example for the 90% central credible interval
-of <code>sigma</code> we would expect the actual coverage to be 75% -
-86%.</p>
+of <code>sigma</code> we would expect the actual coverage to be 73% -
+84%.</p>
 </div>
 <div class="section level2">
 <h2 id="prior-mismatch">Prior mismatch<a class="anchor" aria-label="anchor" href="#prior-mismatch"></a>
@@ -373,7 +376,7 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 model!</p>
 <p>Here we have a generator for a very simple model with gaussian
 likelihood:</p>
-<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb33"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">single_sim_missing</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">N</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="va">mu</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">rnorm</a></span><span class="op">(</span>n <span class="op">=</span> <span class="fl">1</span>, mean <span class="op">=</span> <span class="fl">0</span>, sd <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span>
 <span>  <span class="va">y</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">rnorm</a></span><span class="op">(</span>n <span class="op">=</span> <span class="va">N</span>, mean <span class="op">=</span> <span class="va">mu</span>, sd <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span>
@@ -389,7 +392,7 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 <span><span class="va">datasets_missing</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generate_datasets.html">generate_datasets</a></span><span class="op">(</span><span class="va">generator_missing</span>, n_sims <span class="op">=</span> <span class="fl">200</span><span class="op">)</span></span></code></pre></div>
 <p>And here is a model that just completely ignores the data, but has
 the right prior:</p>
-<div class="sourceCode" id="cb35"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb34"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/readLines.html" class="external-link">readLines</a></span><span class="op">(</span><span class="st">"stan/missing_likelihood.stan"</span><span class="op">)</span>, sep <span class="op">=</span> <span class="st">"\n"</span><span class="op">)</span></span></code></pre></div>
 <pre><code>data {
   int&lt;lower=0&gt; N;
@@ -403,7 +406,7 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 model {
   target += normal_lpdf(mu | 0, 1);
 }</code></pre>
-<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb36"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">iter_warmup</span> <span class="op">&lt;-</span> <span class="fl">300</span></span>
 <span><span class="va">iter_sampling</span> <span class="op">&lt;-</span> <span class="fl">1000</span></span>
 <span></span>
@@ -419,20 +422,20 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 <span>    <span class="va">model_missing</span>, iter <span class="op">=</span> <span class="va">iter_sampling</span> <span class="op">+</span> <span class="va">iter_warmup</span>, warmup <span class="op">=</span> <span class="va">iter_warmup</span>, chains <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <p>Now we’ll compute the results for 200 simulations:</p>
-<div class="sourceCode" id="cb38"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb37"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_missing</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_missing</span>, <span class="va">backend_missing</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"missing"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
 <pre><code><span><span class="co">## Results loaded from cache file 'missing'</span></span></code></pre>
-<pre><code><span><span class="co">##  - 16 (8%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.027.</span></span></code></pre>
+<pre><code><span><span class="co">##  - 15 (8%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.03.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>And here are our rank plots:</p>
-<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb41"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_missing</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb42"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_missing</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_plots-2.png" width="700"></p>
 <p>It’s just nothing out of the ordinary.</p>
@@ -443,7 +446,7 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 we can get the prior sd directly, but one can also use a (preferably
 large) <code>SBC_datasets</code> object to estimate it empirically for
 more complex models.</p>
-<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">prior_sd</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="st">"mu"</span> <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span>
 <span><span class="co">#prior_sd &lt;- calculate_prior_sd(generate_datasets(generator_missing, 1000))</span></span>
 <span><span class="fu"><a href="../reference/plot_contraction.html">plot_contraction</a></span><span class="op">(</span><span class="va">results_missing</span>, <span class="va">prior_sd</span><span class="op">)</span></span></code></pre></div>
@@ -456,37 +459,37 @@ <h2 id="missing-likelihood">Missing likelihood<a class="anchor" aria-label="anch
 <code>plot_sim_estimated</code> showing that the posterior credible
 intervals don’t really change with changes to
 <code>simulated_value</code>.</p>
-<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb44"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">results_missing</span>, alpha <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_sim_estimated-1.png" width="700"></p>
 <p>There is however even more powerful method - and that is to include
-the likelihood in the SBC. This is most easily done by adding a
-“generated quantity” to the SBC results - this is a function that is
-evaluated within the context of the variables AND data. And it can be
-added without recomputing the fits!</p>
-<div class="sourceCode" id="cb46"><pre class="downlit sourceCode r">
+the likelihood in the SBC. This is most easily done by adding a “derived
+quantity” to the SBC results - this is a function that is evaluated
+within the context of the variables AND data. And it can be added
+without recomputing the fits!</p>
+<div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">normal_lpdf</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">y</span>, <span class="va">mu</span>, <span class="va">sigma</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">dnorm</a></span><span class="op">(</span><span class="va">y</span>, mean <span class="op">=</span> <span class="va">mu</span>, sd <span class="op">=</span> <span class="va">sigma</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span>
 <span><span class="op">}</span></span>
 <span></span>
-<span><span class="va">log_lik_gq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generated_quantities.html">generated_quantities</a></span><span class="op">(</span>log_lik <span class="op">=</span> <span class="fu">normal_lpdf</span><span class="op">(</span><span class="va">y</span>, <span class="va">mu</span>, <span class="fl">1</span><span class="op">)</span>, </span>
+<span><span class="va">log_lik_dq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/derived_quantities.html">derived_quantities</a></span><span class="op">(</span>log_lik <span class="op">=</span> <span class="fu">normal_lpdf</span><span class="op">(</span><span class="va">y</span>, <span class="va">mu</span>, <span class="fl">1</span><span class="op">)</span>, </span>
 <span>                                   .globals <span class="op">=</span> <span class="st">"normal_lpdf"</span> <span class="op">)</span></span>
 <span></span>
-<span><span class="va">results_missing_gq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/recompute_SBC_statistics.html">recompute_SBC_statistics</a></span><span class="op">(</span></span>
+<span><span class="va">results_missing_dq</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/recompute_SBC_statistics.html">recompute_SBC_statistics</a></span><span class="op">(</span></span>
 <span>  <span class="va">results_missing</span>, <span class="va">datasets_missing</span>, </span>
-<span>  backend <span class="op">=</span> <span class="va">backend_missing</span>, gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">##  - 19 (10%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.027.</span></span></code></pre>
+<span>  backend <span class="op">=</span> <span class="va">backend_missing</span>, dquants <span class="op">=</span> <span class="va">log_lik_dq</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">##  - 17 (8%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.03.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>The rank plots for the <code>log_lik</code> quantity immediately
 shows a severe problem:</p>
+<div class="sourceCode" id="cb48"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_missing_dq</span><span class="op">)</span></span></code></pre></div>
+<p><img src="limits_of_SBC_files/figure-html/results_missing_dq_plots-1.png" width="700"></p>
 <div class="sourceCode" id="cb49"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_missing_gq</span><span class="op">)</span></span></code></pre></div>
-<p><img src="limits_of_SBC_files/figure-html/results_missing_gq_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_missing_gq</span><span class="op">)</span></span></code></pre></div>
-<p><img src="limits_of_SBC_files/figure-html/results_missing_gq_plots-2.png" width="700"></p>
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_missing_dq</span><span class="op">)</span></span></code></pre></div>
+<p><img src="limits_of_SBC_files/figure-html/results_missing_dq_plots-2.png" width="700"></p>
 </div>
 <div class="section level2">
 <h2 id="partially-missing-likelihood">Partially missing likelihood<a class="anchor" aria-label="anchor" href="#partially-missing-likelihood"></a>
@@ -495,7 +498,7 @@ <h2 id="partially-missing-likelihood">Partially missing likelihood<a class="anch
 (and missing something) - e.g. due to an indexing error. Turns out
 missing just one data point needs a lot of simulations to see, so we’ll
 write a model that ignores a full half of the data points.</p>
-<div class="sourceCode" id="cb51"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/cat.html" class="external-link">cat</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/readLines.html" class="external-link">readLines</a></span><span class="op">(</span><span class="st">"stan/partially_missing_likelihood.stan"</span><span class="op">)</span>, sep <span class="op">=</span> <span class="st">"\n"</span><span class="op">)</span></span></code></pre></div>
 <pre><code>data {
   int&lt;lower=0&gt; N;
@@ -516,7 +519,7 @@ <h2 id="partially-missing-likelihood">Partially missing likelihood<a class="anch
     target += normal_lpdf(y[n] | mu, 1);
   }
 }</code></pre>
-<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb52"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="kw">if</span><span class="op">(</span><span class="va">use_cmdstanr</span><span class="op">)</span> <span class="op">{</span></span>
 <span>  <span class="va">model_missing_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://mc-stan.org/cmdstanr/reference/cmdstan_model.html" class="external-link">cmdstan_model</a></span><span class="op">(</span><span class="st">"stan/partially_missing_likelihood.stan"</span><span class="op">)</span></span>
 <span></span>
@@ -529,33 +532,31 @@ <h2 id="partially-missing-likelihood">Partially missing likelihood<a class="anch
 <span>    <span class="va">model_missing_2</span>, iter <span class="op">=</span> <span class="va">iter_sampling</span> <span class="op">+</span> <span class="va">iter_warmup</span>, warmup <span class="op">=</span> <span class="va">iter_warmup</span>, chains <span class="op">=</span> <span class="fl">1</span><span class="op">)</span></span>
 <span><span class="op">}</span></span></code></pre></div>
 <p>Let us use this model for the same set of simulations.</p>
-<div class="sourceCode" id="cb54"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">results_missing_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_missing</span>, <span class="va">backend_missing_2</span>, gen_quants <span class="op">=</span> <span class="va">log_lik_gq</span>, </span>
+<div class="sourceCode" id="cb53"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">results_missing_2</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_missing</span>, <span class="va">backend_missing_2</span>, dquants <span class="op">=</span> <span class="va">log_lik_dq</span>, </span>
 <span>                    cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
 <span>                    cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"missing_2"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## Results loaded from cache file 'missing_2' but it was computed with different thin_ranks/gen_quants/ensure_num_ranks_divisor.</span></span>
-<span><span class="co">## Calling recompute_SBC_statistics.</span></span></code></pre>
-<pre><code><span><span class="co">##  - 20 (10%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.025.</span></span></code></pre>
+<pre><code><span><span class="co">## Results loaded from cache file 'missing_2'</span></span></code></pre>
+<pre><code><span><span class="co">##  - 17 (8%) fits had at least one Rhat &gt; 1.01. Largest Rhat was 1.035.</span></span></code></pre>
 <pre><code><span><span class="co">## Not all diagnostics are OK.</span></span>
 <span><span class="co">## You can learn more by inspecting $default_diagnostics, $backend_diagnostics </span></span>
 <span><span class="co">## and/or investigating $outputs/$messages/$warnings for detailed output from the backend.</span></span></code></pre>
 <p>The contraction plot would not show anything suspicious - we get
 decent contraction</p>
-<div class="sourceCode" id="cb58"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb57"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_contraction.html">plot_contraction</a></span><span class="op">(</span><span class="va">results_missing_2</span>, <span class="va">prior_sd</span>, variables <span class="op">=</span> <span class="st">"mu"</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_2_contraction-1.png" width="700"></p>
 <p>Similarly, our posterior estimates now cluster around the true
 values.</p>
-<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb58"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_sim_estimated.html">plot_sim_estimated</a></span><span class="op">(</span><span class="va">results_missing_2</span>, variables <span class="op">=</span> <span class="st">"mu"</span>, alpha <span class="op">=</span> <span class="fl">0.5</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_2_sim_estimated-1.png" width="700"></p>
 <p>Now contraction is pretty high, and <code>mu</code> is behaving well,
-but our <code>log_lik</code> generated quantity shows a clear
-problem</p>
-<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
+but our <code>log_lik</code> derived quantity shows a clear problem</p>
+<div class="sourceCode" id="cb59"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_missing_2</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_2_plots-1.png" width="700"></p>
-<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb60"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_missing_2</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_missing_2_plots-2.png" width="700"></p>
 <p>We could definitely find even smaller deviations than omitting half
@@ -586,7 +587,7 @@ <h2 id="incorrect-correlations">Incorrect Correlations<a class="anchor" aria-lab
 <p>We however generate posterior samples from a set of independent
 normal distributions that happen to have the correct mean and standard
 deviation, just the correlation is missing.</p>
-<div class="sourceCode" id="cb62"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb61"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/base/Random.html" class="external-link">set.seed</a></span><span class="op">(</span><span class="fl">546852</span><span class="op">)</span></span>
 <span></span>
 <span><span class="va">mvn_sigma</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/matrix.html" class="external-link">matrix</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>, <span class="fl">0.8</span>,<span class="fl">0.8</span>,<span class="fl">1</span><span class="op">)</span>, nrow <span class="op">=</span> <span class="fl">2</span><span class="op">)</span></span>
@@ -641,38 +642,38 @@ <h2 id="incorrect-correlations">Incorrect Correlations<a class="anchor" aria-lab
 <pre><code><span><span class="co">## Results loaded from cache file 'corr'</span></span></code></pre>
 <p>Although the posterior is incorrect, the default univariate checks
 don’t show any problem even with 1000 simulations.</p>
-<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_corr</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_corr-1.png" width="700"></p>
-<div class="sourceCode" id="cb65"><pre class="downlit sourceCode r">
+<div class="sourceCode" id="cb64"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_corr</span><span class="op">)</span></span></code></pre></div>
 <p><img src="limits_of_SBC_files/figure-html/results_corr-2.png" width="700"></p>
 <p>We can however add derived quantities that depend on both elements of
 mu. We’ll try their sum, difference, product and the multivarite normal
 log likelihood</p>
-<div class="sourceCode" id="cb66"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="va">gq_corr</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/generated_quantities.html">generated_quantities</a></span><span class="op">(</span>sum <span class="op">=</span> <span class="va">mu</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">+</span> <span class="va">mu</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, </span>
+<div class="sourceCode" id="cb65"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="va">dq_corr</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/derived_quantities.html">derived_quantities</a></span><span class="op">(</span>sum <span class="op">=</span> <span class="va">mu</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">+</span> <span class="va">mu</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>, </span>
 <span>                                diff <span class="op">=</span> <span class="va">mu</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">-</span> <span class="va">mu</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>,</span>
 <span>                                prod <span class="op">=</span> <span class="va">mu</span><span class="op">[</span><span class="fl">1</span><span class="op">]</span> <span class="op">*</span> <span class="va">mu</span><span class="op">[</span><span class="fl">2</span><span class="op">]</span>,</span>
 <span>                                mvn_log_lik <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu">mvtnorm</span><span class="fu">::</span><span class="fu"><a href="https://rdrr.io/pkg/mvtnorm/man/Mvnorm.html" class="external-link">dmvnorm</a></span><span class="op">(</span><span class="va">y</span>, mean <span class="op">=</span> <span class="va">mu</span>, sigma <span class="op">=</span> <span class="va">mvn_sigma</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span><span class="op">)</span></span>
 <span></span>
 <span></span>
-<span><span class="va">res_corr_gq</span>  <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_correlated</span>, <span class="va">backend_uncorr</span>, keep_fits <span class="op">=</span> <span class="cn">FALSE</span>,</span>
+<span><span class="va">res_corr_dq</span>  <span class="op">&lt;-</span> <span class="fu"><a href="../reference/compute_SBC.html">compute_SBC</a></span><span class="op">(</span><span class="va">datasets_correlated</span>, <span class="va">backend_uncorr</span>, keep_fits <span class="op">=</span> <span class="cn">FALSE</span>,</span>
 <span>                        globals <span class="op">=</span> <span class="va">analytic_backend_uncorr_globals</span>,</span>
-<span>                        gen_quants <span class="op">=</span> <span class="va">gq_corr</span>,</span>
+<span>                        dquants <span class="op">=</span> <span class="va">dq_corr</span>,</span>
 <span>                        cache_mode <span class="op">=</span> <span class="st">"results"</span>, </span>
-<span>                        cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"corr_gq"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
-<pre><code><span><span class="co">## Results loaded from cache file 'corr_gq'</span></span></code></pre>
+<span>                        cache_location <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/file.path.html" class="external-link">file.path</a></span><span class="op">(</span><span class="va">cache_dir</span>, <span class="st">"corr_dq"</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+<pre><code><span><span class="co">## Results loaded from cache file 'corr_dq'</span></span></code></pre>
 <p>We see that all of the derived quantities show problems, but with
 different strength of signal. We’ll especially note that the log
 likelihood is once again a very good choice, while sum is probably the
 worst of those tested.</p>
+<div class="sourceCode" id="cb67"><pre class="downlit sourceCode r">
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_corr_dq</span><span class="op">)</span></span></code></pre></div>
+<p><img src="limits_of_SBC_files/figure-html/results_corr_dq-1.png" width="700"></p>
 <div class="sourceCode" id="cb68"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">res_corr_gq</span><span class="op">)</span></span></code></pre></div>
-<p><img src="limits_of_SBC_files/figure-html/results_corr_gq-1.png" width="700"></p>
-<div class="sourceCode" id="cb69"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_corr_gq</span><span class="op">)</span></span></code></pre></div>
-<p><img src="limits_of_SBC_files/figure-html/results_corr_gq-2.png" width="700"></p>
+<code class="sourceCode R"><span><span class="fu"><a href="../reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">res_corr_dq</span><span class="op">)</span></span></code></pre></div>
+<p><img src="limits_of_SBC_files/figure-html/results_corr_dq-2.png" width="700"></p>
 </div>
   </div>
 
@@ -693,7 +694,7 @@ <h2 id="incorrect-correlations">Incorrect Correlations<a class="anchor" aria-lab
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
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diff --git a/docs/articles/overview_wide.png b/docs/articles/overview_wide.png
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diff --git a/docs/articles/rank_visualizations.html b/docs/articles/rank_visualizations.html
index ee21aa4..ef090f1 100644
--- a/docs/articles/rank_visualizations.html
+++ b/docs/articles/rank_visualizations.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>SBC rank visualizations</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/rank_visualizations.Rmd" class="external-link"><code>vignettes/rank_visualizations.Rmd</code></a></small>
       <div class="hidden name"><code>rank_visualizations.Rmd</code></div>
@@ -419,7 +419,7 @@ <h2 id="side-by-side-comparison">Side by side comparison<a class="anchor" aria-l
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/rejection_sampling.html b/docs/articles/rejection_sampling.html
index 91836d0..3202771 100644
--- a/docs/articles/rejection_sampling.html
+++ b/docs/articles/rejection_sampling.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Rejection sampling in simulations</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/rejection_sampling.Rmd" class="external-link"><code>vignettes/rejection_sampling.Rmd</code></a></small>
       <div class="hidden name"><code>rejection_sampling.Rmd</code></div>
@@ -151,61 +151,38 @@ <h4 data-toc-skip class="date">2022-07-04</h4>
 certain condition we impose (e.g. that no observed count is larger than
 <span class="math inline">\(10^8\)</span>). But does rejection sampling
 when generating simulations affect the validity of SBC?</p>
-<p>Thanks to forum user Niko Huurre who derived the necessary math at <a href="https://discourse.mc-stan.org/t/using-narrower-priors-for-sbc/21709/6?u=martinmodrak" class="external-link">Stan
-Discourse discussion of the topic</a> we know exactly when it is OK.
-Briefly: for algorithms that only need to know the posterior density up
-to a constant (which includes Stan and many others), it is OK as long as
-the rejection criterion only uses observed data and not the unobserved
-variables.</p>
+<p>It turns out that it does not as long as the rejection criterion only
+uses observed data and not the unobserved variables.</p>
 <p>We’ll first walk through the math and then show examples of both OK
 and problematic rejection sampling.</p>
 <div class="section level2">
 <h2 id="the-math">The math<a class="anchor" aria-label="anchor" href="#the-math"></a>
 </h2>
-<p>Let <span class="math inline">\(f\left(y\right)\)</span> be the
-probability that the simulated data <span class="math inline">\(y\)</span> is rejected (usually a 0-1 function if
-you have a clear idea what a “bad” dataset looks like, but could be
-probabilistic if you’re relying on finicky diagnostics). The important
-numbers are the probability of rejection for variable <span class="math inline">\(\theta\)</span></p>
+<p>Let <span class="math inline">\(\mathtt{accept}(y)\)</span> be the
+probability the the simulated data <span class="math inline">\(y\)</span> is accepted. Note that <span class="math inline">\(\mathtt{accept}\)</span> uses only data as input
+and would usually be a 0-1 function if you have a clear idea what a
+“bad” dataset looks like, but could be probabilistic if you’re relying
+on finicky diagnostics.</p>
+<p>We define a variable <span class="math inline">\(a \sim
+\text{Bernoulli}(\mathtt{accept}(y))\)</span>. Given the parameter space
+<span class="math inline">\(\Theta\)</span> and a specific <span class="math inline">\(\theta \in \Theta\)</span>, this implies a joint
+distribution <span class="math inline">\(\pi(\theta, y, a)\)</span> that
+factorizes as <span class="math inline">\(\pi(\theta, y, a) =
+\pi(a|y)\pi(y | \theta)\pi(\theta)\)</span>. We can then look at the
+posterior conditional on accepting a dataset to see the claimed
+invariance:</p>
 <p><span class="math display">\[
-L\left(\theta\right)=\int
-f\left(y\right)\pi\left(y|\theta\right)\mathrm{d}y
+\begin{equation}
+\pi(\theta | y, a = 1) = \frac{\pi(a = 1 | y) \pi(y |
+\theta)\pi(\theta)}{\int_\Theta \mathrm{d}\tilde\theta \: \pi(a = 1 | y)
+\pi(y | \tilde\theta)\pi(\tilde\theta)} =
+\frac{\pi(y | \theta)\pi(\theta)}{\int_\Theta \mathrm{d}\tilde\theta \:
+\pi(y | \tilde\theta)\pi(\tilde\theta)} = \pi(\theta | y)
+\end{equation}
 \]</span></p>
-<p>and the total rate of rejections from the prior</p>
-<p><span class="math display">\[
-R=\iint
-f\left(y\right)\pi\left(y|\theta\right)\pi\left(\theta\right)\mathrm{d}y\mathrm{d}\theta=\int
-L\left(\theta\right)\pi\left(\theta\right)\mathrm{d}\theta
-\]</span></p>
-<p>Rejecting the simulation when it generates “bad” data effectively
-distorts the prior</p>
-<p><span class="math display">\[
-\pi\left(\theta\right)\to\frac{L\left(\theta\right)}{R}\pi\left(\theta\right)
-\]</span></p>
-<p>and of course rejections change the generating distribution</p>
-<p><span class="math display">\[
-\pi\left(y|\theta\right)\to\frac{f\left(y\right)}{L\left(\theta\right)}\pi\left(y|\theta\right)
-\]</span></p>
-<p>but crucially these changes cancel out when computing the posterior.
-Before rejections we have:</p>
-<p><span class="math display">\[
-\pi(\theta | y) \propto \pi(y | \theta) \pi(\theta)
-\]</span></p>
-<p>After rejections we have</p>
-<p><span class="math display">\[
-\pi(\theta | y) \propto \frac{L(\theta)}{R} \pi(y | \theta)
-\frac{f(y)}{L(\theta)} \pi(\theta) = \frac{f(y)}{R} \pi(y | \theta)
-\pi(\theta)
-\]</span></p>
-<p>And since <span class="math inline">\(\frac{f(y)}{R}\)</span> is a
-constant for any given simulation (and hence the fit), the overall
-posterior for Stan (and most other MCMC algorithms) is the same, because
-Stan only needs the posterior density up to a constant. So whether we
-take rejection into account or not, the model will match the generating
-process. However, if <span class="math inline">\(f\)</span> also
-depended on <span class="math inline">\(\theta\)</span>, it would no
-longer contribute a constant and we’ll get a mismatch between the
-generator and model.</p>
+<p>So whether we take rejection into account or not, the model will
+match the generating process. However, if <span class="math inline">\(\mathtt{accept}\)</span> also depended on <span class="math inline">\(\theta\)</span>, it would no longer contribute a
+constant and we’ll get a mismatch between the generator and model.</p>
 </div>
 <div class="section level2">
 <h2 id="practical-examples">Practical examples<a class="anchor" aria-label="anchor" href="#practical-examples"></a>
@@ -408,7 +385,7 @@ <h2 id="take-home-message">Take home message<a class="anchor" aria-label="anchor
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/small_model_workflow.html b/docs/articles/small_model_workflow.html
index e018bc8..943ea25 100644
--- a/docs/articles/small_model_workflow.html
+++ b/docs/articles/small_model_workflow.html
@@ -33,7 +33,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -127,7 +127,7 @@ <h1 data-toc-skip>Small model implementation workflow</h1>
                         <h4 data-toc-skip class="author">Martin
 Modrák</h4>
             
-            <h4 data-toc-skip class="date">2022-07-04</h4>
+            <h4 data-toc-skip class="date">2022-12-15</h4>
       
       <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/vignettes/small_model_workflow.Rmd" class="external-link"><code>vignettes/small_model_workflow.Rmd</code></a></small>
       <div class="hidden name"><code>small_model_workflow.Rmd</code></div>
@@ -528,16 +528,16 @@ <h3 id="fixing-ordering">Fixing ordering<a class="anchor" aria-label="anchor" hr
 <div class="sourceCode" id="cb43"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="va">results_fixed_ordered</span><span class="op">$</span><span class="va">backend_diagnostics</span></span></code></pre></div>
 <pre><code><span><span class="co">##    sim_id max_chain_time n_failed_chains n_divergent n_max_treedepth n_rejects</span></span>
-<span><span class="co">## 1       1          0.505               0           7               0         0</span></span>
-<span><span class="co">## 2       2          0.715               0         145               0         0</span></span>
-<span><span class="co">## 3       3          0.539               0           0               0         0</span></span>
-<span><span class="co">## 4       4          0.461               0           0               0         0</span></span>
-<span><span class="co">## 5       5          2.524               0           0               0         0</span></span>
-<span><span class="co">## 6       6          0.723               0           0               0         0</span></span>
+<span><span class="co">## 1       1          0.484               0           7               0         0</span></span>
+<span><span class="co">## 2       2          0.777               0         145               0         0</span></span>
+<span><span class="co">## 3       3          0.556               0           0               0         0</span></span>
+<span><span class="co">## 4       4          0.501               0           0               0         0</span></span>
+<span><span class="co">## 5       5          2.629               0           0               0         0</span></span>
+<span><span class="co">## 6       6          0.665               0           0               0         0</span></span>
 <span><span class="co">## 7       7          0.498               0           0               0         0</span></span>
-<span><span class="co">## 8       8          0.440               0           0               0         0</span></span>
-<span><span class="co">## 9       9          0.361               0           0               0         0</span></span>
-<span><span class="co">## 10     10          0.354               0           0               0         0</span></span></code></pre>
+<span><span class="co">## 8       8          0.455               0           0               0         0</span></span>
+<span><span class="co">## 9       9          0.376               0           0               0         0</span></span>
+<span><span class="co">## 10     10          0.374               0           0               0         0</span></span></code></pre>
 <p>One of the fits has quite a lot of divergent transitions. Let’s look
 at the pairs plot for the model:</p>
 <div class="sourceCode" id="cb45"><pre class="downlit sourceCode r">
@@ -612,7 +612,7 @@ <h3 id="fixing-degenerate-components">Fixing degenerate components?<a class="anc
 <span><span class="co">##  - No fits had divergent transitions.</span></span>
 <span><span class="co">##  - No fits had iterations that saturated max treedepth.</span></span>
 <span><span class="co">##  - No fits had steps rejected.</span></span>
-<span><span class="co">##  - Maximum time per chain was 2.524 sec.</span></span></code></pre>
+<span><span class="co">##  - Maximum time per chain was 2.629 sec.</span></span></code></pre>
 <p>This gives us no obvious problems.</p>
 <div class="sourceCode" id="cb50"><pre class="downlit sourceCode r">
 <code class="sourceCode R"><span><span class="fu"><a href="../reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_fixed_ordered_subset</span><span class="op">)</span></span></code></pre></div>
@@ -695,7 +695,7 @@ <h3 id="fixing-degenerate-components">Fixing degenerate components?<a class="anc
 <span><span class="co">##  - No fits had divergent transitions.</span></span>
 <span><span class="co">##  - No fits had iterations that saturated max treedepth.</span></span>
 <span><span class="co">##  - No fits had steps rejected.</span></span>
-<span><span class="co">##  - Maximum time per chain was 4.253 sec.</span></span></code></pre>
+<span><span class="co">##  - Maximum time per chain was 4.316 sec.</span></span></code></pre>
 <p>And we can use <code>bind_results</code> to combine the new results
 with the previous fits to not waste our computational effort.</p>
 <div class="sourceCode" id="cb63"><pre class="downlit sourceCode r">
@@ -1482,7 +1482,7 @@ <h2 id="take-home-message">Take home message<a class="anchor" aria-label="anchor
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_coverage-1.png b/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_coverage-1.png
index 78d5434..79a9ecc 100644
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diff --git a/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_plots-1.png b/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_plots-1.png
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diff --git a/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_plots-2.png b/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_200_plots-2.png
index a0c9f8a..673473e 100644
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diff --git a/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_plots-1.png b/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_plots-1.png
index 6d456cc..b34b715 100644
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diff --git a/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_plots-2.png b/docs/articles/small_model_workflow_files/figure-html/results_beta_precision_fixed_prior_plots-2.png
index e8866b2..81935c8 100644
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diff --git a/docs/authors.html b/docs/authors.html
index 20e849d..cd6fde9 100644
--- a/docs/authors.html
+++ b/docs/authors.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -150,7 +150,7 @@ <h1 id="citation">Citation</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/index.html b/docs/index.html
index e1a6259..296afd2 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -36,7 +36,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -134,7 +134,7 @@ <h2 id="installation">Installation<a class="anchor" aria-label="anchor" href="#i
 </h2>
 <p>To install the development version of SBC, run</p>
 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
-<code class="sourceCode R"><span><span class="fu">devtools</span><span class="fu">::</span><span class="fu">install_github</span><span class="op">(</span><span class="st">"hyunjimoon/SBC"</span><span class="op">)</span></span></code></pre></div>
+<code class="sourceCode R"><span><span class="fu">devtools</span><span class="fu">::</span><span class="fu"><a href="https://remotes.r-lib.org/reference/install_github.html" class="external-link">install_github</a></span><span class="op">(</span><span class="st">"hyunjimoon/SBC"</span><span class="op">)</span></span></code></pre></div>
 </div>
 <div class="section level2">
 <h2 id="quick-tour">Quick tour<a class="anchor" aria-label="anchor" href="#quick-tour"></a>
@@ -163,7 +163,7 @@ <h2 id="quick-tour">Quick tour<a class="anchor" aria-label="anchor" href="#quick
 <span></span>
 <span><span class="fu"><a href="reference/plot_rank_hist.html">plot_rank_hist</a></span><span class="op">(</span><span class="va">results_sd</span><span class="op">)</span></span>
 <span><span class="fu"><a href="reference/ECDF-plots.html">plot_ecdf_diff</a></span><span class="op">(</span><span class="va">results_sd</span><span class="op">)</span></span></code></pre></div>
-<p>The diagnostic plots show no problems in this case. As with any other software test, we can observe clear failures, but absence of failures does not imply correctness. We can however make the SBC check more thorough by using a lot of simulations and including suitable generated quantities to guard against <a href="https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html">known limitations of vanilla SBC</a>.</p>
+<p>The diagnostic plots show no problems in this case. As with any other software test, we can observe clear failures, but absence of failures does not imply correctness. We can however make the SBC check more thorough by using a lot of simulations and including suitable derived quantities to guard against <a href="https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html">known limitations of vanilla SBC</a>.</p>
 </div>
 <div class="section level2">
 <h2 id="paralellization">Paralellization<a class="anchor" aria-label="anchor" href="#paralellization"></a>
@@ -192,7 +192,9 @@ <h2 id="references">References<a class="anchor" aria-label="anchor" href="#refer
 <li>Theoretical support
 <ul>
 <li>
-<a href="https://arxiv.org/pdf/1804.06788.pdf" class="external-link">Validating Bayesian Inference Algorithms with Simulation-Based Calibration</a> Talts, Betancourt, Simpson, Vehtari, Gelman, 2018</li>
+<a href="https://arxiv.org/abs/2211.02383v1" class="external-link">Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity</a> Modrák, Moon, Kim, Bürkner, Huurre, Faltejsková, Gelman, Vehtari, 2022</li>
+<li>
+<a href="http://www.stat.columbia.edu/~gelman/research/unpublished/sbc.pdf" class="external-link">Validating Bayesian Inference Algorithms with Simulation-Based Calibration</a> Talts, Betancourt, Simpson, Vehtari, Gelman, 2018</li>
 <li>
 <a href="https://arxiv.org/abs/2103.10522" class="external-link">Graphical Test for Discrete Uniformity and its Applications in Goodness of Fit Evaluation and Multiple Sample Comparison</a> Säilynoja, Bürkner, Vehtari, 2021</li>
 <li>
@@ -278,7 +280,7 @@ <h2 data-toc-skip>Developers</h2>
 
 <div class="pkgdown">
   <p></p>
-<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+<p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer>
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
index 5feb8fb..ece5d2c 100644
--- a/docs/pkgdown.yml
+++ b/docs/pkgdown.yml
@@ -1,5 +1,5 @@
-pandoc: 2.17.1.1
-pkgdown: 2.0.5
+pandoc: 2.19.2
+pkgdown: 2.0.6
 pkgdown_sha: ~
 articles:
   bad_parametrization: bad_parametrization.html
@@ -13,7 +13,7 @@ articles:
   rejection_sampling: rejection_sampling.html
   SBC: SBC.html
   small_model_workflow: small_model_workflow.html
-last_built: 2022-07-04T11:54Z
+last_built: 2022-12-15T13:30Z
 urls:
   reference: https://hyunjimoon.github.io/SBC/reference
   article: https://hyunjimoon.github.io/SBC/articles
diff --git a/docs/reference/ECDF-plots.html b/docs/reference/ECDF-plots.html
index d13b62e..b8e7563 100644
--- a/docs/reference/ECDF-plots.html
+++ b/docs/reference/ECDF-plots.html
@@ -19,7 +19,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -200,7 +200,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/Rplot001.png b/docs/reference/Rplot001.png
new file mode 100644
index 0000000..17a3580
Binary files /dev/null and b/docs/reference/Rplot001.png differ
diff --git a/docs/reference/SBC-deprecated.html b/docs/reference/SBC-deprecated.html
index a6ac4be..a5dac6f 100644
--- a/docs/reference/SBC-deprecated.html
+++ b/docs/reference/SBC-deprecated.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -102,7 +102,7 @@
   <div class="col-md-9 contents">
     <div class="page-header">
     <h1>Deprecated functions in package <span class="pkg">SBC</span>.</h1>
-    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/SBC-deprecated.R" class="external-link"><code>R/SBC-deprecated.R</code></a>, <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/results.R" class="external-link"><code>R/results.R</code></a></small>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/SBC-deprecated.R" class="external-link"><code>R/SBC-deprecated.R</code></a>, <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a>, <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/results.R" class="external-link"><code>R/results.R</code></a></small>
     <div class="hidden name"><code>SBC-deprecated.Rd</code></div>
     </div>
 
@@ -114,11 +114,43 @@ <h1>Deprecated functions in package <span class="pkg">SBC</span>.</h1>
     </div>
 
     <div id="ref-usage">
-    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">compute_results</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">generated_quantities</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">validate_generated_quantities</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">bind_generated_quantities</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">compute_gen_quants</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
+<span></span>
+<span><span class="fu">compute_results</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu">recompute_statistics</span><span class="op">(</span><span class="va">...</span><span class="op">)</span></span></code></pre></div>
     </div>
 
+    <div id="generated-quantities">
+    <h2><code>generated_quantities</code></h2>
+    
+
+<p>Instead of <code>generated_quantities</code>, use <code><a href="derived_quantities.html">derived_quantities</a></code>.</p>
+    </div>
+    <div id="validate-generated-quantities">
+    <h2><code>validate_generated_quantities</code></h2>
+    
+
+<p>Instead of <code>validate_generated_quantities</code>, use <code><a href="validate_derived_quantities.html">validate_derived_quantities</a></code>.</p>
+    </div>
+    <div id="bind-generated-quantities">
+    <h2><code>bind_generated_quantities</code></h2>
+    
+
+<p>Instead of <code>bind_generated_quantities</code>, use <code><a href="bind_derived_quantities.html">bind_derived_quantities</a></code>.</p>
+    </div>
+    <div id="compute-gen-quants">
+    <h2><code>compute_gen_quants</code></h2>
+    
+
+<p>Instead of <code>compute_gen_quants</code>, use <code><a href="compute_dquants.html">compute_dquants</a></code>.</p>
+    </div>
     <div id="compute-results">
     <h2><code>compute_results</code></h2>
     
@@ -144,7 +176,7 @@ <h2><code>recompute_statistics</code></h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_brms.html b/docs/reference/SBC_backend_brms.html
index b4721fe..b39569a 100644
--- a/docs/reference/SBC_backend_brms.html
+++ b/docs/reference/SBC_backend_brms.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -139,7 +139,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_brms_from_generator.html b/docs/reference/SBC_backend_brms_from_generator.html
index 10cecbf..e06b124 100644
--- a/docs/reference/SBC_backend_brms_from_generator.html
+++ b/docs/reference/SBC_backend_brms_from_generator.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -129,7 +129,7 @@ <h1>Build a brms backend, reusing the compiled model from a previously created <
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_cmdstan_sample.html b/docs/reference/SBC_backend_cmdstan_sample.html
index 74e20cd..f35554b 100644
--- a/docs/reference/SBC_backend_cmdstan_sample.html
+++ b/docs/reference/SBC_backend_cmdstan_sample.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -136,7 +136,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_cmdstan_variational.html b/docs/reference/SBC_backend_cmdstan_variational.html
index fae605b..89db017 100644
--- a/docs/reference/SBC_backend_cmdstan_variational.html
+++ b/docs/reference/SBC_backend_cmdstan_variational.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -143,7 +143,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_default_thin_ranks.html b/docs/reference/SBC_backend_default_thin_ranks.html
index 99cd9e7..64c7fcf 100644
--- a/docs/reference/SBC_backend_default_thin_ranks.html
+++ b/docs/reference/SBC_backend_default_thin_ranks.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -129,7 +129,7 @@ <h1>S3 generic to get backend-specific default thinning for rank computation.</h
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_hash_for_cache.html b/docs/reference/SBC_backend_hash_for_cache.html
index f3783ce..7bc16af 100644
--- a/docs/reference/SBC_backend_hash_for_cache.html
+++ b/docs/reference/SBC_backend_hash_for_cache.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -126,7 +126,7 @@ <h1>Get hash used to identify cached results.</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_iid_draws.html b/docs/reference/SBC_backend_iid_draws.html
index 56085b4..991f809 100644
--- a/docs/reference/SBC_backend_iid_draws.html
+++ b/docs/reference/SBC_backend_iid_draws.html
@@ -24,7 +24,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -147,7 +147,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_mock.html b/docs/reference/SBC_backend_mock.html
index 4b7be02..8717d7e 100644
--- a/docs/reference/SBC_backend_mock.html
+++ b/docs/reference/SBC_backend_mock.html
@@ -19,7 +19,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -140,7 +140,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_rjags.html b/docs/reference/SBC_backend_rjags.html
index 02c2549..859a272 100644
--- a/docs/reference/SBC_backend_rjags.html
+++ b/docs/reference/SBC_backend_rjags.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -163,7 +163,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_rstan_optimizing.html b/docs/reference/SBC_backend_rstan_optimizing.html
index aa89a37..c3d854d 100644
--- a/docs/reference/SBC_backend_rstan_optimizing.html
+++ b/docs/reference/SBC_backend_rstan_optimizing.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_backend_rstan_sample.html b/docs/reference/SBC_backend_rstan_sample.html
index 580104c..c277008 100644
--- a/docs/reference/SBC_backend_rstan_sample.html
+++ b/docs/reference/SBC_backend_rstan_sample.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -136,7 +136,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_datasets.html b/docs/reference/SBC_datasets.html
index 6a7fc37..f02566e 100644
--- a/docs/reference/SBC_datasets.html
+++ b/docs/reference/SBC_datasets.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_example_backend.html b/docs/reference/SBC_example_backend.html
index 7146d39..9d26d4e 100644
--- a/docs/reference/SBC_example_backend.html
+++ b/docs/reference/SBC_example_backend.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -144,7 +144,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_example_generator.html b/docs/reference/SBC_example_generator.html
index adfa705..635cd9c 100644
--- a/docs/reference/SBC_example_generator.html
+++ b/docs/reference/SBC_example_generator.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_example_results.html b/docs/reference/SBC_example_results.html
index bf6dc84..b43fe35 100644
--- a/docs/reference/SBC_example_results.html
+++ b/docs/reference/SBC_example_results.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -160,7 +160,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_fit.html b/docs/reference/SBC_fit.html
index 8e761fb..60dbfd8 100644
--- a/docs/reference/SBC_fit.html
+++ b/docs/reference/SBC_fit.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -130,7 +130,7 @@ <h1>S3 generic using backend to fit a model to data.</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_fit_to_diagnostics.html b/docs/reference/SBC_fit_to_diagnostics.html
index 2738a90..4fb1fef 100644
--- a/docs/reference/SBC_fit_to_diagnostics.html
+++ b/docs/reference/SBC_fit_to_diagnostics.html
@@ -19,7 +19,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -152,7 +152,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_fit_to_draws_matrix.html b/docs/reference/SBC_fit_to_draws_matrix.html
index 319beeb..e47bbb7 100644
--- a/docs/reference/SBC_fit_to_draws_matrix.html
+++ b/docs/reference/SBC_fit_to_draws_matrix.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -133,7 +133,7 @@ <h1>S3 generic converting a fitted model to a <code>draws_matrix</code> object.<
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_generator_brms.html b/docs/reference/SBC_generator_brms.html
index d43ae74..8ff6802 100644
--- a/docs/reference/SBC_generator_brms.html
+++ b/docs/reference/SBC_generator_brms.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -138,7 +138,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_generator_custom.html b/docs/reference/SBC_generator_custom.html
index 2dfdec0..ab01fe9 100644
--- a/docs/reference/SBC_generator_custom.html
+++ b/docs/reference/SBC_generator_custom.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -126,10 +126,12 @@ <h2>Arguments</h2>
 </dl></div>
     <div id="details">
     <h2>Details</h2>
-    <p>Running:</p><div class="sourceCode r"><pre><code>gen &lt;- SBC_generator_custom(f, &lt;&lt;some other args&gt;&gt;)
+    <p>Running:</p>
+<p></p><div class="sourceCode r"><pre><code>gen &lt;- SBC_generator_custom(f, &lt;&lt;some other args&gt;&gt;)
 datasets &lt;- generate_datasets(gen, n_sims = my_n_sims)
 </code></pre><p></p></div>
-<p>is equivalent to just running</p><div class="sourceCode r"><pre><code>datasets &lt;- f(&lt;&lt;some other args&gt;&gt;, n_sims = my_n_sims)
+<p>is equivalent to just running</p>
+<p></p><div class="sourceCode r"><pre><code>datasets &lt;- f(&lt;&lt;some other args&gt;&gt;, n_sims = my_n_sims)
 </code></pre><p></p></div>
 <p>So whenever you control the code calling <code>generate_datasets</code>,
 it usually makes more sense to just create an <code>SBC_datasets</code>
@@ -151,7 +153,7 @@ <h2>Details</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_generator_function.html b/docs/reference/SBC_generator_function.html
index a03ca45..fc7208e 100644
--- a/docs/reference/SBC_generator_function.html
+++ b/docs/reference/SBC_generator_function.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -136,7 +136,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_print_example_model.html b/docs/reference/SBC_print_example_model.html
index 6a935f0..b2b1c3d 100644
--- a/docs/reference/SBC_print_example_model.html
+++ b/docs/reference/SBC_print_example_model.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -133,7 +133,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_results.html b/docs/reference/SBC_results.html
index 0ec0188..8b03d4a 100644
--- a/docs/reference/SBC_results.html
+++ b/docs/reference/SBC_results.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Details</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/SBC_statistics_from_single_fit.html b/docs/reference/SBC_statistics_from_single_fit.html
index 9cae47c..c75297a 100644
--- a/docs/reference/SBC_statistics_from_single_fit.html
+++ b/docs/reference/SBC_statistics_from_single_fit.html
@@ -19,7 +19,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -118,8 +118,9 @@ <h1>Recompute SBC statistics given a single fit.</h1>
 <span>  <span class="va">generated</span>,</span>
 <span>  <span class="va">thin_ranks</span>,</span>
 <span>  <span class="va">ensure_num_ranks_divisor</span>,</span>
-<span>  <span class="va">gen_quants</span>,</span>
-<span>  <span class="va">backend</span></span>
+<span>  <span class="va">dquants</span>,</span>
+<span>  <span class="va">backend</span>,</span>
+<span>  gen_quants <span class="op">=</span> <span class="cn">NULL</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
@@ -136,6 +137,10 @@ <h2>Arguments</h2>
 ensure that this number divides the total number of SBC ranks (see Details).</p></dd>
 
 
+<dt>dquants</dt>
+<dd><p>Derived quantities to include in SBC. Use <code><a href="derived_quantities.html">derived_quantities()</a></code> to construct them.</p></dd>
+
+
 <dt>backend</dt>
 <dd><p>the model + sampling algorithm. The built-in backends can be constructed
 using <code><a href="SBC_backend_cmdstan_sample.html">SBC_backend_cmdstan_sample()</a></code>, <code><a href="SBC_backend_cmdstan_variational.html">SBC_backend_cmdstan_variational()</a></code>,
@@ -143,6 +148,10 @@ <h2>Arguments</h2>
 (more to come: issue 31, 38, 39). The backend is an S3 class supporting at least the <code><a href="SBC_fit.html">SBC_fit()</a></code>,
 <code><a href="SBC_fit_to_draws_matrix.html">SBC_fit_to_draws_matrix()</a></code> methods.</p></dd>
 
+
+<dt>gen_quants</dt>
+<dd><p>Deprecated, use dquants instead</p></dd>
+
 </dl></div>
     <div id="see-also">
     <h2>See also</h2>
@@ -161,7 +170,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/bind_datasets.html b/docs/reference/bind_datasets.html
index 2f9f628..a518a54 100644
--- a/docs/reference/bind_datasets.html
+++ b/docs/reference/bind_datasets.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -130,7 +130,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/bind_derived_quantities.html b/docs/reference/bind_derived_quantities.html
new file mode 100644
index 0000000..b880e94
--- /dev/null
+++ b/docs/reference/bind_derived_quantities.html
@@ -0,0 +1,138 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Combine two lists of derived quantities — bind_derived_quantities • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Combine two lists of derived quantities — bind_derived_quantities"><meta property="og:description" content="Combine two lists of derived quantities"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Combine two lists of derived quantities</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>bind_derived_quantities.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Combine two lists of derived quantities</p>
+    </div>
+
+    <div id="ref-usage">
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">bind_derived_quantities</span><span class="op">(</span><span class="va">dq1</span>, <span class="va">dq2</span><span class="op">)</span></span></code></pre></div>
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+
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diff --git a/docs/reference/bind_generated_quantities-deprecated.html b/docs/reference/bind_generated_quantities-deprecated.html
new file mode 100644
index 0000000..1975ef2
--- /dev/null
+++ b/docs/reference/bind_generated_quantities-deprecated.html
@@ -0,0 +1,139 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Combine two lists of derived quantities — bind_generated_quantities-deprecated • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Combine two lists of derived quantities — bind_generated_quantities-deprecated"><meta property="og:description" content="Delegates directly to bind_derived_quantities()."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+
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+    <div class="page-header">
+    <h1>Combine two lists of derived quantities</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>bind_generated_quantities-deprecated.Rd</code></div>
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+
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+    <p>Delegates directly to <code><a href="bind_derived_quantities.html">bind_derived_quantities()</a></code>.</p>
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+
+
+    <div id="see-also">
+    <h2>See also</h2>
+    <div class="dont-index"><p><code><a href="SBC-deprecated.html">SBC-deprecated</a></code></p></div>
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+
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+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
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diff --git a/docs/reference/bind_globals.html b/docs/reference/bind_globals.html
new file mode 100644
index 0000000..9d55206
--- /dev/null
+++ b/docs/reference/bind_globals.html
@@ -0,0 +1,142 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Combine two sets globals for use in derived quantities or backend — bind_globals • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Combine two sets globals for use in derived quantities or backend — bind_globals"><meta property="og:description" content="Combine two sets globals for use in derived quantities or backend"><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+    
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+        <a class="navbar-link" href="../index.html">SBC</a>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
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+      <a href="http://paul-buerkner.github.io/brms/" class="external-link">brms</a>
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+      <a href="http://mc-stan.org/rstanarm" class="external-link">rstanarm</a>
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+      <a href="http://mc-stan.org/bayesplot" class="external-link">bayesplot</a>
+    </li>
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+      <a href="http://mc-stan.org/shinystan" class="external-link">shinystan</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/loo" class="external-link">loo</a>
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+      <a href="http://mc-stan.org/projpred" class="external-link">projpred</a>
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+      <a href="https://mc-stan.org/posterior" class="external-link">posterior</a>
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+  <a href="http://mc-stan.org" class="external-link">Stan</a>
+</li>
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+  <a href="http://discourse.mc-stan.org/" class="external-link">
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+
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+
+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Combine two sets globals for use in derived quantities or backend</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/results.R" class="external-link"><code>R/results.R</code></a></small>
+    <div class="hidden name"><code>bind_globals.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Combine two sets globals for use in derived quantities or backend</p>
+    </div>
+
+    <div id="ref-usage">
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">bind_globals</span><span class="op">(</span><span class="va">globals1</span>, <span class="va">globals2</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div id="see-also">
+    <h2>See also</h2>
+    <div class="dont-index"><p><code><a href="compute_SBC.html">compute_SBC()</a></code>, <code><a href="derived_quantities.html">derived_quantities()</a></code></p></div>
+    </div>
+
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
+
+      </footer></div>
+
+  
+
+
+  
+
+  </body></html>
+
diff --git a/docs/reference/bind_results.html b/docs/reference/bind_results.html
index 55b7e78..faf68dd 100644
--- a/docs/reference/bind_results.html
+++ b/docs/reference/bind_results.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -134,7 +134,7 @@ <h2>Details</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/calculate_prior_sd.html b/docs/reference/calculate_prior_sd.html
index a85731c..6d9b246 100644
--- a/docs/reference/calculate_prior_sd.html
+++ b/docs/reference/calculate_prior_sd.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -130,7 +130,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/calculate_ranks_draws_matrix.html b/docs/reference/calculate_ranks_draws_matrix.html
index 908b5d0..6e59e19 100644
--- a/docs/reference/calculate_ranks_draws_matrix.html
+++ b/docs/reference/calculate_ranks_draws_matrix.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -140,7 +140,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/check_all_SBC_diagnostics.html b/docs/reference/check_all_SBC_diagnostics.html
index 26e3797..785396b 100644
--- a/docs/reference/check_all_SBC_diagnostics.html
+++ b/docs/reference/check_all_SBC_diagnostics.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -136,7 +136,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/cjs_dist.html b/docs/reference/cjs_dist.html
index 280d286..b144c45 100644
--- a/docs/reference/cjs_dist.html
+++ b/docs/reference/cjs_dist.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -179,7 +179,7 @@ <h2>References</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/combine_args.html b/docs/reference/combine_args.html
index 5d2cc63..a8d0735 100644
--- a/docs/reference/combine_args.html
+++ b/docs/reference/combine_args.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -129,7 +129,7 @@ <h1>Combine two named lists and overwrite elements with the same name
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/compute_SBC.html b/docs/reference/compute_SBC.html
index 6990266..8244479 100644
--- a/docs/reference/compute_SBC.html
+++ b/docs/reference/compute_SBC.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -116,10 +116,11 @@ <h1>Fit datasets and evaluate diagnostics and SBC metrics.</h1>
 <span>  thin_ranks <span class="op">=</span> <span class="fu"><a href="SBC_backend_default_thin_ranks.html">SBC_backend_default_thin_ranks</a></span><span class="op">(</span><span class="va">backend</span><span class="op">)</span>,</span>
 <span>  ensure_num_ranks_divisor <span class="op">=</span> <span class="fl">2</span>,</span>
 <span>  chunk_size <span class="op">=</span> <span class="fu"><a href="default_chunk_size.html">default_chunk_size</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/base/length.html" class="external-link">length</a></span><span class="op">(</span><span class="va">datasets</span><span class="op">)</span><span class="op">)</span>,</span>
-<span>  gen_quants <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  dquants <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  cache_mode <span class="op">=</span> <span class="st">"none"</span>,</span>
 <span>  cache_location <span class="op">=</span> <span class="cn">NULL</span>,</span>
-<span>  globals <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span></span>
+<span>  globals <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span>,</span>
+<span>  gen_quants <span class="op">=</span> <span class="cn">NULL</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
@@ -174,6 +175,10 @@ <h2>Arguments</h2>
 See documentation of <code>future.chunk.size</code> argument for <code><a href="https://future.apply.futureverse.org/reference/future_lapply.html" class="external-link">future.apply::future_lapply()</a></code> for more details.</p></dd>
 
 
+<dt>dquants</dt>
+<dd><p>Derived quantities to include in SBC. Use <code><a href="derived_quantities.html">derived_quantities()</a></code> to construct them.</p></dd>
+
+
 <dt>cache_mode</dt>
 <dd><p>Type of caching of results, currently the only supported modes are
 <code>"none"</code> (do not cache) and <code>"results"</code> where the whole results object is stored
@@ -193,6 +198,10 @@ <h2>Arguments</h2>
 It is added to the <code>globals</code> argument to <code><a href="https://future.futureverse.org/reference/future.html" class="external-link">future::future()</a></code>, to make those
 objects available on all workers.</p></dd>
 
+
+<dt>gen_quants</dt>
+<dd><p>Deprecated, use dquants instead</p></dd>
+
 </dl></div>
     <div id="value">
     <h2>Value</h2>
@@ -253,7 +262,7 @@ <h2>Rank divisors</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/compute_dquants.html b/docs/reference/compute_dquants.html
new file mode 100644
index 0000000..f33ee50
--- /dev/null
+++ b/docs/reference/compute_dquants.html
@@ -0,0 +1,144 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Compute derived quantities based on given data and posterior draws. — compute_dquants • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Compute derived quantities based on given data and posterior draws. — compute_dquants"><meta property="og:description" content="Compute derived quantities based on given data and posterior draws."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
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+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
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+      <span class="navbar-brand">
+        <a class="navbar-link" href="../index.html">SBC</a>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
+      </span>
+    </div>
+
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+  <a href="../articles/SBC.html">Get Started</a>
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+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
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+    </li>
+    <li>
+      <a href="http://paul-buerkner.github.io/brms/" class="external-link">brms</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstanarm" class="external-link">rstanarm</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/bayesplot" class="external-link">bayesplot</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/shinystan" class="external-link">shinystan</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/loo" class="external-link">loo</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/projpred" class="external-link">projpred</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstantools" class="external-link">rstantools</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/posterior" class="external-link">posterior</a>
+    </li>
+  </ul></li>
+<li>
+  <a href="http://mc-stan.org" class="external-link">Stan</a>
+</li>
+      </ul><ul class="nav navbar-nav navbar-right"><li>
+  <a href="https://twitter.com/mcmc_stan" class="external-link">
+    <span class="fa fa-twitter"></span>
+     
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+</li>
+<li>
+  <a href="https://github.com/hyunjimoon/SBC" class="external-link">
+    <span class="fa fa-github"></span>
+     
+  </a>
+</li>
+<li>
+  <a href="http://discourse.mc-stan.org/" class="external-link">
+    <span class="fa fa-users"></span>
+     
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+      </ul></div><!--/.nav-collapse -->
+  </div><!--/.container -->
+</div><!--/.navbar -->
+
+      
+
+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Compute derived quantities based on given data and posterior draws.</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>compute_dquants.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Compute derived quantities based on given data and posterior draws.</p>
+    </div>
+
+    <div id="ref-usage">
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">compute_dquants</span><span class="op">(</span><span class="va">draws</span>, <span class="va">generated</span>, <span class="va">dquants</span>, gen_quants <span class="op">=</span> <span class="cn">NULL</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div id="arguments">
+    <h2>Arguments</h2>
+    <dl><dt>gen_quants</dt>
+<dd><p>Deprecated, use <code>dquants</code></p></dd>
+
+</dl></div>
+
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
+
+      </footer></div>
+
+  
+
+
+  
+
+  </body></html>
+
diff --git a/docs/reference/compute_gen_quants-deprecated.html b/docs/reference/compute_gen_quants-deprecated.html
new file mode 100644
index 0000000..d0db3b2
--- /dev/null
+++ b/docs/reference/compute_gen_quants-deprecated.html
@@ -0,0 +1,139 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Compute derived quantities based on given data and posterior draws. — compute_gen_quants-deprecated • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Compute derived quantities based on given data and posterior draws. — compute_gen_quants-deprecated"><meta property="og:description" content="Delegates directly to compute_dquants()."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+    
+
+    <div class="container template-reference-topic">
+      <header><div class="navbar navbar-default navbar-fixed-top" role="navigation">
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+      <span class="navbar-brand">
+        <a class="navbar-link" href="../index.html">SBC</a>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
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+
+    <div id="navbar" class="navbar-collapse collapse">
+      <ul class="nav navbar-nav"><li>
+  <a href="../articles/SBC.html">Get Started</a>
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+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
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+  <ul class="dropdown-menu" role="menu"><li>
+      <a href="http://mc-stan.org/rstan" class="external-link">rstan</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/cmdstanr" class="external-link">cmdstanr</a>
+    </li>
+    <li>
+      <a href="http://paul-buerkner.github.io/brms/" class="external-link">brms</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstanarm" class="external-link">rstanarm</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/bayesplot" class="external-link">bayesplot</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/shinystan" class="external-link">shinystan</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/loo" class="external-link">loo</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/projpred" class="external-link">projpred</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstantools" class="external-link">rstantools</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/posterior" class="external-link">posterior</a>
+    </li>
+  </ul></li>
+<li>
+  <a href="http://mc-stan.org" class="external-link">Stan</a>
+</li>
+      </ul><ul class="nav navbar-nav navbar-right"><li>
+  <a href="https://twitter.com/mcmc_stan" class="external-link">
+    <span class="fa fa-twitter"></span>
+     
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+</li>
+<li>
+  <a href="https://github.com/hyunjimoon/SBC" class="external-link">
+    <span class="fa fa-github"></span>
+     
+  </a>
+</li>
+<li>
+  <a href="http://discourse.mc-stan.org/" class="external-link">
+    <span class="fa fa-users"></span>
+     
+  </a>
+</li>
+      </ul></div><!--/.nav-collapse -->
+  </div><!--/.container -->
+</div><!--/.navbar -->
+
+      
+
+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Compute derived quantities based on given data and posterior draws.</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>compute_gen_quants-deprecated.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Delegates directly to <code><a href="compute_dquants.html">compute_dquants()</a></code>.</p>
+    </div>
+
+
+    <div id="see-also">
+    <h2>See also</h2>
+    <div class="dont-index"><p><code><a href="SBC-deprecated.html">SBC-deprecated</a></code></p></div>
+    </div>
+
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
+
+      </footer></div>
+
+  
+
+
+  
+
+  </body></html>
+
diff --git a/docs/reference/compute_results-deprecated.html b/docs/reference/compute_results-deprecated.html
index 62e5386..1ebc0d1 100644
--- a/docs/reference/compute_results-deprecated.html
+++ b/docs/reference/compute_results-deprecated.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -125,7 +125,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/data_for_ecdf_plots.html b/docs/reference/data_for_ecdf_plots.html
index cbd68e2..8e6c418 100644
--- a/docs/reference/data_for_ecdf_plots.html
+++ b/docs/reference/data_for_ecdf_plots.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -124,7 +124,7 @@ <h1>Maybe not export in the end? Useful for debugging</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/default_chunk_size.html b/docs/reference/default_chunk_size.html
index 190e621..18293cd 100644
--- a/docs/reference/default_chunk_size.html
+++ b/docs/reference/default_chunk_size.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -130,7 +130,7 @@ <h1>Determines the default chunk size.</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/default_cores_per_fit.html b/docs/reference/default_cores_per_fit.html
index 0a1a5c2..acf6c35 100644
--- a/docs/reference/default_cores_per_fit.html
+++ b/docs/reference/default_cores_per_fit.html
@@ -20,7 +20,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -134,7 +134,7 @@ <h1>Determines the default cores per single fit.</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/derived_quantities.html b/docs/reference/derived_quantities.html
new file mode 100644
index 0000000..afbded1
--- /dev/null
+++ b/docs/reference/derived_quantities.html
@@ -0,0 +1,174 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Create a definition of derived quantities evaluated in R. — derived_quantities • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Create a definition of derived quantities evaluated in R. — derived_quantities"><meta property="og:description" content="When the expression contains non-library functions/objects, and parallel processing
+is enabled, those must be
+named in the .globals parameter (hopefully we'll be able to detect those
+automatically in the future). Note that recompute_SBC_statistics() currently
+does not use parallel processing, so .globals don't need to be set."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+    
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+      <a href="http://mc-stan.org/rstan" class="external-link">rstan</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/cmdstanr" class="external-link">cmdstanr</a>
+    </li>
+    <li>
+      <a href="http://paul-buerkner.github.io/brms/" class="external-link">brms</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstanarm" class="external-link">rstanarm</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/bayesplot" class="external-link">bayesplot</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/shinystan" class="external-link">shinystan</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/loo" class="external-link">loo</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/projpred" class="external-link">projpred</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstantools" class="external-link">rstantools</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/posterior" class="external-link">posterior</a>
+    </li>
+  </ul></li>
+<li>
+  <a href="http://mc-stan.org" class="external-link">Stan</a>
+</li>
+      </ul><ul class="nav navbar-nav navbar-right"><li>
+  <a href="https://twitter.com/mcmc_stan" class="external-link">
+    <span class="fa fa-twitter"></span>
+     
+  </a>
+</li>
+<li>
+  <a href="https://github.com/hyunjimoon/SBC" class="external-link">
+    <span class="fa fa-github"></span>
+     
+  </a>
+</li>
+<li>
+  <a href="http://discourse.mc-stan.org/" class="external-link">
+    <span class="fa fa-users"></span>
+     
+  </a>
+</li>
+      </ul></div><!--/.nav-collapse -->
+  </div><!--/.container -->
+</div><!--/.navbar -->
+
+      
+
+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Create a definition of derived quantities evaluated in R.</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>derived_quantities.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>When the expression contains non-library functions/objects, and parallel processing
+is enabled, those must be
+named in the <code>.globals</code> parameter (hopefully we'll be able to detect those
+automatically in the future). Note that <code><a href="recompute_SBC_statistics.html">recompute_SBC_statistics()</a></code> currently
+does not use parallel processing, so <code>.globals</code> don't need to be set.</p>
+    </div>
+
+    <div id="ref-usage">
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">derived_quantities</span><span class="op">(</span><span class="va">...</span>, .globals <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/list.html" class="external-link">list</a></span><span class="op">(</span><span class="op">)</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+    <div id="arguments">
+    <h2>Arguments</h2>
+    <dl><dt>...</dt>
+<dd><p>named expressions representing the quantitites</p></dd>
+
+
+<dt>.globals</dt>
+<dd><p>A list of names of objects that are defined
+in the global environment and need to present for the gen. quants. to evaluate.
+It is added to the <code>globals</code> argument to <code><a href="https://future.futureverse.org/reference/future.html" class="external-link">future::future()</a></code>, to make those
+objects available on all workers.</p></dd>
+
+</dl></div>
+
+    <div id="ref-examples">
+    <h2>Examples</h2>
+    <div class="sourceCode"><pre class="sourceCode r"><code><span class="r-in"><span><span class="co"># Derived quantity computing the total log likelihood of a normal distribution</span></span></span>
+<span class="r-in"><span><span class="co"># with known sd = 1</span></span></span>
+<span class="r-in"><span><span class="va">normal_lpdf</span> <span class="op">&lt;-</span> <span class="kw">function</span><span class="op">(</span><span class="va">y</span>, <span class="va">mu</span>, <span class="va">sigma</span><span class="op">)</span> <span class="op">{</span></span></span>
+<span class="r-in"><span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="fu"><a href="https://rdrr.io/r/stats/Normal.html" class="external-link">dnorm</a></span><span class="op">(</span><span class="va">y</span>, mean <span class="op">=</span> <span class="va">mu</span>, sd <span class="op">=</span> <span class="va">sigma</span>, log <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span><span class="op">)</span></span></span>
+<span class="r-in"><span><span class="op">}</span></span></span>
+<span class="r-in"><span></span></span>
+<span class="r-in"><span><span class="co"># Note the use of .globals to make the normal_lpdf function available</span></span></span>
+<span class="r-in"><span><span class="co"># within the expression</span></span></span>
+<span class="r-in"><span><span class="va">log_lik_dq</span> <span class="op">&lt;-</span> <span class="fu">derived_quantities</span><span class="op">(</span>log_lik <span class="op">=</span> <span class="fu">normal_lpdf</span><span class="op">(</span><span class="va">y</span>, <span class="va">mu</span>, <span class="fl">1</span><span class="op">)</span>,</span></span>
+<span class="r-in"><span>                                .globals <span class="op">=</span> <span class="st">"normal_lpdf"</span> <span class="op">)</span></span></span>
+<span class="r-in"><span></span></span>
+</code></pre></div>
+    </div>
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
+
+      </footer></div>
+
+  
+
+
+  
+
+  </body></html>
+
diff --git a/docs/reference/empirical_coverage.html b/docs/reference/empirical_coverage.html
index 95df6e0..f0f65cc 100644
--- a/docs/reference/empirical_coverage.html
+++ b/docs/reference/empirical_coverage.html
@@ -23,7 +23,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -182,7 +182,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/generate_datasets.html b/docs/reference/generate_datasets.html
index 95e4cf2..d1a7eeb 100644
--- a/docs/reference/generate_datasets.html
+++ b/docs/reference/generate_datasets.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -148,7 +148,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/generated_quantities-deprecated.html b/docs/reference/generated_quantities-deprecated.html
new file mode 100644
index 0000000..6a917d4
--- /dev/null
+++ b/docs/reference/generated_quantities-deprecated.html
@@ -0,0 +1,142 @@
+<!DOCTYPE html>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Create a definition of derived quantities evaluated in R. — generated_quantities-deprecated • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Create a definition of derived quantities evaluated in R. — generated_quantities-deprecated"><meta property="og:description" content="Delegates directly to derived_quantities().
+Delegates directly to validate_derived_quantities()."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
+<script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
+<![endif]--></head><body data-spy="scroll" data-target="#toc">
+    
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+      </button>
+      <span class="navbar-brand">
+        <a class="navbar-link" href="../index.html">SBC</a>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
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+    <div id="navbar" class="navbar-collapse collapse">
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+  <a href="../articles/SBC.html">Get Started</a>
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+  <a href="../reference/index.html">Functions</a>
+</li>
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+  <a href="#" class="dropdown-toggle" data-toggle="dropdown" role="button" data-bs-toggle="dropdown" aria-expanded="false">
+    Other Packages
+     
+    <span class="caret"></span>
+  </a>
+  <ul class="dropdown-menu" role="menu"><li>
+      <a href="http://mc-stan.org/rstan" class="external-link">rstan</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/cmdstanr" class="external-link">cmdstanr</a>
+    </li>
+    <li>
+      <a href="http://paul-buerkner.github.io/brms/" class="external-link">brms</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstanarm" class="external-link">rstanarm</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/bayesplot" class="external-link">bayesplot</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/shinystan" class="external-link">shinystan</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/loo" class="external-link">loo</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/projpred" class="external-link">projpred</a>
+    </li>
+    <li>
+      <a href="http://mc-stan.org/rstantools" class="external-link">rstantools</a>
+    </li>
+    <li>
+      <a href="https://mc-stan.org/posterior" class="external-link">posterior</a>
+    </li>
+  </ul></li>
+<li>
+  <a href="http://mc-stan.org" class="external-link">Stan</a>
+</li>
+      </ul><ul class="nav navbar-nav navbar-right"><li>
+  <a href="https://twitter.com/mcmc_stan" class="external-link">
+    <span class="fa fa-twitter"></span>
+     
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+</li>
+<li>
+  <a href="https://github.com/hyunjimoon/SBC" class="external-link">
+    <span class="fa fa-github"></span>
+     
+  </a>
+</li>
+<li>
+  <a href="http://discourse.mc-stan.org/" class="external-link">
+    <span class="fa fa-users"></span>
+     
+  </a>
+</li>
+      </ul></div><!--/.nav-collapse -->
+  </div><!--/.container -->
+</div><!--/.navbar -->
+
+      
+
+      </header><div class="row">
+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Create a definition of derived quantities evaluated in R.</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>generated_quantities-deprecated.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Delegates directly to <code><a href="derived_quantities.html">derived_quantities()</a></code>.</p>
+<p>Delegates directly to <code><a href="validate_derived_quantities.html">validate_derived_quantities()</a></code>.</p>
+    </div>
+
+
+    <div id="see-also">
+    <h2>See also</h2>
+    <div class="dont-index"><p><code><a href="SBC-deprecated.html">SBC-deprecated</a></code></p>
+<p><code><a href="SBC-deprecated.html">SBC-deprecated</a></code></p></div>
+    </div>
+
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
+
+      </footer></div>
+
+  
+
+
+  
+
+  </body></html>
+
diff --git a/docs/reference/get_diagnostic_messages.html b/docs/reference/get_diagnostic_messages.html
index 9a874fa..a5dd320 100644
--- a/docs/reference/get_diagnostic_messages.html
+++ b/docs/reference/get_diagnostic_messages.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -130,7 +130,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/guess_rank_hist_bins.html b/docs/reference/guess_rank_hist_bins.html
index 4b4660f..c5be918 100644
--- a/docs/reference/guess_rank_hist_bins.html
+++ b/docs/reference/guess_rank_hist_bins.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -134,7 +134,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/index.html b/docs/reference/index.html
index 8c441ce..635164d 100644
--- a/docs/reference/index.html
+++ b/docs/reference/index.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -219,9 +219,25 @@ <h2 id="computation-results">Computation &amp; results <a href="#computation-res
         </td>
         <td><p>Subset the results.</p></td>
       </tr><tr><td>
-          <p><code><a href="generated_quantities.html">generated_quantities()</a></code> </p>
+          <p><code><a href="bind_derived_quantities.html">bind_derived_quantities()</a></code> </p>
         </td>
-        <td><p>Create a definition of generated quantities evaluated in R.</p></td>
+        <td><p>Combine two lists of derived quantities</p></td>
+      </tr><tr><td>
+          <p><code><a href="derived_quantities.html">derived_quantities()</a></code> </p>
+        </td>
+        <td><p>Create a definition of derived quantities evaluated in R.</p></td>
+      </tr><tr><td>
+          <p><code><a href="validate_derived_quantities.html">validate_derived_quantities()</a></code> </p>
+        </td>
+        <td><p>Validate a definition of derived quantities evaluated in R.</p></td>
+      </tr><tr><td>
+          <p><code><a href="compute_dquants.html">compute_dquants()</a></code> </p>
+        </td>
+        <td><p>Compute derived quantities based on given data and posterior draws.</p></td>
+      </tr><tr><td>
+          <p><code><a href="bind_globals.html">bind_globals()</a></code> </p>
+        </td>
+        <td><p>Combine two sets globals for use in derived quantities or backend</p></td>
       </tr><tr><td>
           <p><code><a href="SBC_statistics_from_single_fit.html">SBC_statistics_from_single_fit()</a></code> </p>
         </td>
@@ -285,7 +301,7 @@ <h2 id="plotting-summarising">Plotting &amp; Summarising <a href="#plotting-summ
       </tr><tr><td>
           <p><code><a href="guess_rank_hist_bins.html">guess_rank_hist_bins()</a></code> </p>
         </td>
-        <td><p>Guess the number of bins for <code><a href="../reference/plot_rank_hist.html">plot_rank_hist()</a></code>.</p></td>
+        <td><p>Guess the number of bins for <code><a href="https://hyunjimoon.github.io/SBC/reference/plot_rank_hist.html">plot_rank_hist()</a></code>.</p></td>
       </tr><tr><td>
           <p><code><a href="empirical_coverage.html">empirical_coverage()</a></code> </p>
         </td>
@@ -353,7 +369,7 @@ <h2 id="miscellaneous">Miscellaneous <a href="#miscellaneous" class="anchor" ari
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/max_diff.html b/docs/reference/max_diff.html
index d72695f..46169bd 100644
--- a/docs/reference/max_diff.html
+++ b/docs/reference/max_diff.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -144,7 +144,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/plot_contraction.html b/docs/reference/plot_contraction.html
index 049509b..c2cc12a 100644
--- a/docs/reference/plot_contraction.html
+++ b/docs/reference/plot_contraction.html
@@ -19,7 +19,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -171,7 +171,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/plot_coverage.html b/docs/reference/plot_coverage.html
index b455aa8..44c12a8 100644
--- a/docs/reference/plot_coverage.html
+++ b/docs/reference/plot_coverage.html
@@ -23,7 +23,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -125,7 +125,8 @@ <h1>Plot the observed coverage and its uncertainty.</h1>
 <span>  variables <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  prob <span class="op">=</span> <span class="fl">0.95</span>,</span>
 <span>  interval_type <span class="op">=</span> <span class="st">"central"</span>,</span>
-<span>  parameters <span class="op">=</span> <span class="cn">NULL</span></span>
+<span>  parameters <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  max_points <span class="op">=</span> <span class="cn">NULL</span></span>
 <span><span class="op">)</span></span>
 <span></span>
 <span><span class="fu">plot_coverage_diff</span><span class="op">(</span></span>
@@ -133,7 +134,8 @@ <h1>Plot the observed coverage and its uncertainty.</h1>
 <span>  variables <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  prob <span class="op">=</span> <span class="fl">0.95</span>,</span>
 <span>  interval_type <span class="op">=</span> <span class="st">"central"</span>,</span>
-<span>  parameters <span class="op">=</span> <span class="cn">NULL</span></span>
+<span>  parameters <span class="op">=</span> <span class="cn">NULL</span>,</span>
+<span>  max_points <span class="op">=</span> <span class="cn">NULL</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
 
@@ -154,6 +156,12 @@ <h2>Arguments</h2>
 <dt>parameters</dt>
 <dd><p>DEPRECATED. Use <code>variables</code> instead.</p></dd>
 
+
+<dt>max_points</dt>
+<dd><p>maximum number of points where to evaluate the coverage.
+If set to <code>NULL</code>, coverage is evaluated across the whole range of ranks.
+Setting to some smaller number may reduce memory footprint and increase speed.</p></dd>
+
 </dl></div>
     <div id="value">
     <h2>Value</h2>
@@ -178,7 +186,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/plot_rank_hist.html b/docs/reference/plot_rank_hist.html
index fe221e4..4abf288 100644
--- a/docs/reference/plot_rank_hist.html
+++ b/docs/reference/plot_rank_hist.html
@@ -22,7 +22,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -165,7 +165,7 @@ <h2>Details</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/plot_sim_estimated.html b/docs/reference/plot_sim_estimated.html
index 77a0349..be8623a 100644
--- a/docs/reference/plot_sim_estimated.html
+++ b/docs/reference/plot_sim_estimated.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -165,7 +165,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/rank2unif.html b/docs/reference/rank2unif.html
index f1288b7..891399c 100644
--- a/docs/reference/rank2unif.html
+++ b/docs/reference/rank2unif.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/rdunif.html b/docs/reference/rdunif.html
index d10e673..36b408d 100644
--- a/docs/reference/rdunif.html
+++ b/docs/reference/rdunif.html
@@ -18,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -126,7 +126,7 @@ <h1>Discrete uniform distribution allowing for varying lower and upper bounds.</
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/recompute_SBC_statistics.html b/docs/reference/recompute_SBC_statistics.html
index 9a0bcbd..abdfa88 100644
--- a/docs/reference/recompute_SBC_statistics.html
+++ b/docs/reference/recompute_SBC_statistics.html
@@ -1,5 +1,6 @@
 <!DOCTYPE html>
-<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Recompute SBC statistics without refitting models. — recompute_SBC_statistics • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Recompute SBC statistics without refitting models. — recompute_SBC_statistics"><meta property="og:description" content="Recompute SBC statistics without refitting models."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
+<!-- Generated by pkgdown: do not edit by hand --><html lang="en"><head><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta charset="utf-8"><meta http-equiv="X-UA-Compatible" content="IE=edge"><meta name="viewport" content="width=device-width, initial-scale=1.0"><title>Recompute SBC statistics without refitting models. — recompute_SBC_statistics • SBC</title><!-- jquery --><script src="https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min.js" integrity="sha256-CSXorXvZcTkaix6Yvo6HppcZGetbYMGWSFlBw8HfCJo=" crossorigin="anonymous"></script><!-- Bootstrap --><link href="https://cdnjs.cloudflare.com/ajax/libs/bootswatch/3.4.0/cosmo/bootstrap.min.css" rel="stylesheet" crossorigin="anonymous"><script src="https://cdnjs.cloudflare.com/ajax/libs/twitter-bootstrap/3.4.1/js/bootstrap.min.js" integrity="sha256-nuL8/2cJ5NDSSwnKD8VqreErSWHtnEP9E7AySL+1ev4=" crossorigin="anonymous"></script><!-- bootstrap-toc --><link rel="stylesheet" href="../bootstrap-toc.css"><script src="../bootstrap-toc.js"></script><!-- Font Awesome icons --><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/all.min.css" integrity="sha256-mmgLkCYLUQbXn0B1SRqzHar6dCnv9oZFPEC1g1cwlkk=" crossorigin="anonymous"><link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.12.1/css/v4-shims.min.css" integrity="sha256-wZjR52fzng1pJHwx4aV2AO3yyTOXrcDW7jBpJtTwVxw=" crossorigin="anonymous"><!-- clipboard.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/clipboard.js/2.0.6/clipboard.min.js" integrity="sha256-inc5kl9MA1hkeYUt+EC3BhlIgyp/2jDIyBLS6k3UxPI=" crossorigin="anonymous"></script><!-- headroom.js --><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/headroom.min.js" integrity="sha256-AsUX4SJE1+yuDu5+mAVzJbuYNPHj/WroHuZ8Ir/CkE0=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/headroom/0.11.0/jQuery.headroom.min.js" integrity="sha256-ZX/yNShbjqsohH1k95liqY9Gd8uOiE1S4vZc+9KQ1K4=" crossorigin="anonymous"></script><!-- pkgdown --><link href="../pkgdown.css" rel="stylesheet"><script src="../pkgdown.js"></script><meta property="og:title" content="Recompute SBC statistics without refitting models. — recompute_SBC_statistics"><meta property="og:description" content="Useful for example to recompute SBC ranks with a different choice of thin_ranks
+or added derived quantities."><!-- mathjax --><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js" integrity="sha256-nvJJv9wWKEm88qvoQl9ekL2J+k/RWIsaSScxxlsrv8k=" crossorigin="anonymous"></script><script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/config/TeX-AMS-MML_HTMLorMML.js" integrity="sha256-84DKXVJXs0/F8OTMzX4UR909+jtl4G7SPypPavF+GfA=" crossorigin="anonymous"></script><!--[if lt IE 9]>
 <script src="https://oss.maxcdn.com/html5shiv/3.7.3/html5shiv.min.js"></script>
 <script src="https://oss.maxcdn.com/respond/1.4.2/respond.min.js"></script>
 <![endif]--></head><body data-spy="scroll" data-target="#toc">
@@ -17,7 +18,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -104,7 +105,8 @@ <h1>Recompute SBC statistics without refitting models.</h1>
     </div>
 
     <div class="ref-description">
-    <p>Recompute SBC statistics without refitting models.</p>
+    <p>Useful for example to recompute SBC ranks with a different choice of <code>thin_ranks</code>
+or added derived quantities.</p>
     </div>
 
     <div id="ref-usage">
@@ -114,6 +116,7 @@ <h1>Recompute SBC statistics without refitting models.</h1>
 <span>  <span class="va">backend</span>,</span>
 <span>  thin_ranks <span class="op">=</span> <span class="fu"><a href="SBC_backend_default_thin_ranks.html">SBC_backend_default_thin_ranks</a></span><span class="op">(</span><span class="va">backend</span><span class="op">)</span>,</span>
 <span>  ensure_num_ranks_divisor <span class="op">=</span> <span class="fl">2</span>,</span>
+<span>  dquants <span class="op">=</span> <span class="cn">NULL</span>,</span>
 <span>  gen_quants <span class="op">=</span> <span class="cn">NULL</span></span>
 <span><span class="op">)</span></span></code></pre></div>
     </div>
@@ -139,6 +142,14 @@ <h2>Arguments</h2>
 <dd><p>Potentially drop some posterior samples to
 ensure that this number divides the total number of SBC ranks (see Details).</p></dd>
 
+
+<dt>dquants</dt>
+<dd><p>Derived quantities to include in SBC. Use <code><a href="derived_quantities.html">derived_quantities()</a></code> to construct them.</p></dd>
+
+
+<dt>gen_quants</dt>
+<dd><p>Deprecated, use dquants instead</p></dd>
+
 </dl></div>
     <div id="value">
     <h2>Value</h2>
@@ -146,11 +157,6 @@ <h2>Value</h2>
 
 <p>An S3 object of class <code>SBC_results</code> with updated <code>$stats</code> and <code>$default_diagnostics</code> fields.</p>
     </div>
-    <div id="details">
-    <h2>Details</h2>
-    <p>Useful for example to recompute SBC ranks with a different choice of <code>thin_ranks</code>
-or added generated quantities.</p>
-    </div>
 
   </div>
   <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
@@ -164,7 +170,7 @@ <h2>Details</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/recompute_statistics-deprecated.html b/docs/reference/recompute_statistics-deprecated.html
index 93e17ed..a775529 100644
--- a/docs/reference/recompute_statistics-deprecated.html
+++ b/docs/reference/recompute_statistics-deprecated.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -125,7 +125,7 @@ <h2>See also</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/set2set.html b/docs/reference/set2set.html
index fd0285e..acbdf12 100644
--- a/docs/reference/set2set.html
+++ b/docs/reference/set2set.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -142,7 +142,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/sub-.SBC_datasets.html b/docs/reference/sub-.SBC_datasets.html
index f63b771..edafe91 100644
--- a/docs/reference/sub-.SBC_datasets.html
+++ b/docs/reference/sub-.SBC_datasets.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -125,7 +125,7 @@ <h1>Subset an <code>SBC_datasets</code> object.</h1>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/sub-.SBC_results.html b/docs/reference/sub-.SBC_results.html
index c4749d8..492fc48 100644
--- a/docs/reference/sub-.SBC_results.html
+++ b/docs/reference/sub-.SBC_results.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -132,7 +132,7 @@ <h2>Arguments</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/reference/validate_derived_quantities.html b/docs/reference/validate_derived_quantities.html
new file mode 100644
index 0000000..4e75033
--- /dev/null
+++ b/docs/reference/validate_derived_quantities.html
@@ -0,0 +1,138 @@
+<!DOCTYPE html>
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+  <div class="col-md-9 contents">
+    <div class="page-header">
+    <h1>Validate a definition of derived quantities evaluated in R.</h1>
+    <small class="dont-index">Source: <a href="https://github.com/hyunjimoon/SBC/blob/HEAD/R/derived-quantities.R" class="external-link"><code>R/derived-quantities.R</code></a></small>
+    <div class="hidden name"><code>validate_derived_quantities.Rd</code></div>
+    </div>
+
+    <div class="ref-description">
+    <p>Validate a definition of derived quantities evaluated in R.</p>
+    </div>
+
+    <div id="ref-usage">
+    <div class="sourceCode"><pre class="sourceCode r"><code><span><span class="fu">validate_derived_quantities</span><span class="op">(</span><span class="va">x</span><span class="op">)</span></span></code></pre></div>
+    </div>
+
+
+  </div>
+  <div class="col-md-3 hidden-xs hidden-sm" id="pkgdown-sidebar">
+    <nav id="toc" data-toggle="toc" class="sticky-top"><h2 data-toc-skip>Contents</h2>
+    </nav></div>
+</div>
+
+
+      <footer><div class="copyright">
+  <p></p><p>Developed by Shinyoung Kim, Hyunji Moon, Martin Modrák, Teemu Säilynoja.</p>
+</div>
+
+<div class="pkgdown">
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
+</div>
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diff --git a/docs/reference/wasserstein.html b/docs/reference/wasserstein.html
index d232b6f..495c6ac 100644
--- a/docs/reference/wasserstein.html
+++ b/docs/reference/wasserstein.html
@@ -17,7 +17,7 @@
       </button>
       <span class="navbar-brand">
         <a class="navbar-link" href="../index.html">SBC</a>
-        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.1.1.9000</span>
+        <span class="version label label-default" data-toggle="tooltip" data-placement="bottom" title="">0.2.0.9000</span>
       </span>
     </div>
 
@@ -144,7 +144,7 @@ <h2>Value</h2>
 </div>
 
 <div class="pkgdown">
-  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.5.</p>
+  <p></p><p>Site built with <a href="https://pkgdown.r-lib.org/" class="external-link">pkgdown</a> 2.0.6.</p>
 </div>
 
       </footer></div>
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
index a067956..f09eea3 100644
--- a/docs/sitemap.xml
+++ b/docs/sitemap.xml
@@ -54,6 +54,15 @@
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/bind_datasets.html</loc>
   </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/bind_derived_quantities.html</loc>
+  </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/bind_generated_quantities-deprecated.html</loc>
+  </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/bind_globals.html</loc>
+  </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/bind_results.html</loc>
   </url>
@@ -72,6 +81,12 @@
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/combine_args.html</loc>
   </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/compute_dquants.html</loc>
+  </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/compute_gen_quants-deprecated.html</loc>
+  </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/compute_results-deprecated.html</loc>
   </url>
@@ -87,12 +102,18 @@
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/default_cores_per_fit.html</loc>
   </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/derived_quantities.html</loc>
+  </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/ECDF-plots.html</loc>
   </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/empirical_coverage.html</loc>
   </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/generated_quantities-deprecated.html</loc>
+  </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/generated_quantities.html</loc>
   </url>
@@ -219,6 +240,9 @@
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/sub-.SBC_results.html</loc>
   </url>
+  <url>
+    <loc>https://hyunjimoon.github.io/SBC/reference/validate_derived_quantities.html</loc>
+  </url>
   <url>
     <loc>https://hyunjimoon.github.io/SBC/reference/wasserstein.html</loc>
   </url>
diff --git a/man/SBC-deprecated.Rd b/man/SBC-deprecated.Rd
index 711aff2..6bb3614 100644
--- a/man/SBC-deprecated.Rd
+++ b/man/SBC-deprecated.Rd
@@ -1,11 +1,24 @@
 % Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/SBC-deprecated.R, R/results.R
+% Please edit documentation in R/SBC-deprecated.R, R/derived-quantities.R,
+%   R/results.R
 \name{SBC-deprecated}
 \alias{SBC-deprecated}
+\alias{generated_quantities}
+\alias{validate_generated_quantities}
+\alias{bind_generated_quantities}
+\alias{compute_gen_quants}
 \alias{compute_results}
 \alias{recompute_statistics}
 \title{Deprecated functions in package \pkg{SBC}.}
 \usage{
+generated_quantities(...)
+
+validate_generated_quantities(...)
+
+bind_generated_quantities(...)
+
+compute_gen_quants(...)
+
 compute_results(...)
 
 recompute_statistics(...)
@@ -16,6 +29,26 @@ the near future. When possible, alternative functions with similar
 functionality are also mentioned. Help pages for deprecated functions are
 available at \code{help("<function>-deprecated")}.
 }
+\section{\code{generated_quantities}}{
+
+Instead of \code{generated_quantities}, use \code{\link{derived_quantities}}.
+}
+
+\section{\code{validate_generated_quantities}}{
+
+Instead of \code{validate_generated_quantities}, use \code{\link{validate_derived_quantities}}.
+}
+
+\section{\code{bind_generated_quantities}}{
+
+Instead of \code{bind_generated_quantities}, use \code{\link{bind_derived_quantities}}.
+}
+
+\section{\code{compute_gen_quants}}{
+
+Instead of \code{compute_gen_quants}, use \code{\link{compute_dquants}}.
+}
+
 \section{\code{compute_results}}{
 
 Instead of \code{compute_results}, use \code{\link{compute_SBC}}.
diff --git a/man/SBC_statistics_from_single_fit.Rd b/man/SBC_statistics_from_single_fit.Rd
index d750ca2..970957a 100644
--- a/man/SBC_statistics_from_single_fit.Rd
+++ b/man/SBC_statistics_from_single_fit.Rd
@@ -10,8 +10,9 @@ SBC_statistics_from_single_fit(
   generated,
   thin_ranks,
   ensure_num_ranks_divisor,
-  gen_quants,
-  backend
+  dquants,
+  backend,
+  gen_quants = NULL
 )
 }
 \arguments{
@@ -22,11 +23,15 @@ thinned draws See details below.}
 \item{ensure_num_ranks_divisor}{Potentially drop some posterior samples to
 ensure that this number divides the total number of SBC ranks (see Details).}
 
+\item{dquants}{Derived quantities to include in SBC. Use \code{\link[=derived_quantities]{derived_quantities()}} to construct them.}
+
 \item{backend}{the model + sampling algorithm. The built-in backends can be constructed
 using \code{\link[=SBC_backend_cmdstan_sample]{SBC_backend_cmdstan_sample()}}, \code{\link[=SBC_backend_cmdstan_variational]{SBC_backend_cmdstan_variational()}},
 \code{\link[=SBC_backend_rstan_sample]{SBC_backend_rstan_sample()}}, \code{\link[=SBC_backend_rstan_optimizing]{SBC_backend_rstan_optimizing()}} and \code{\link[=SBC_backend_brms]{SBC_backend_brms()}}.
 (more to come: issue 31, 38, 39). The backend is an S3 class supporting at least the \code{\link[=SBC_fit]{SBC_fit()}},
 \code{\link[=SBC_fit_to_draws_matrix]{SBC_fit_to_draws_matrix()}} methods.}
+
+\item{gen_quants}{Deprecated, use dquants instead}
 }
 \description{
 Potentially useful for doing some advanced stuff, but should not
diff --git a/man/bind_derived_quantities.Rd b/man/bind_derived_quantities.Rd
new file mode 100644
index 0000000..20efbb2
--- /dev/null
+++ b/man/bind_derived_quantities.Rd
@@ -0,0 +1,11 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{bind_derived_quantities}
+\alias{bind_derived_quantities}
+\title{Combine two lists of derived quantities}
+\usage{
+bind_derived_quantities(dq1, dq2)
+}
+\description{
+Combine two lists of derived quantities
+}
diff --git a/man/bind_generated_quantities-deprecated.Rd b/man/bind_generated_quantities-deprecated.Rd
new file mode 100644
index 0000000..4dbdf9d
--- /dev/null
+++ b/man/bind_generated_quantities-deprecated.Rd
@@ -0,0 +1,12 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{bind_generated_quantities-deprecated}
+\alias{bind_generated_quantities-deprecated}
+\title{Combine two lists of derived quantities}
+\description{
+Delegates directly to \code{bind_derived_quantities()}.
+}
+\seealso{
+\code{\link{SBC-deprecated}}
+}
+\keyword{internal}
diff --git a/man/bind_globals.Rd b/man/bind_globals.Rd
index 0cbb2bb..5986e6a 100644
--- a/man/bind_globals.Rd
+++ b/man/bind_globals.Rd
@@ -2,10 +2,13 @@
 % Please edit documentation in R/results.R
 \name{bind_globals}
 \alias{bind_globals}
-\title{Bind globals used in gen quants or backend}
+\title{Combine two sets globals for use in derived quantities or backend}
 \usage{
 bind_globals(globals1, globals2)
 }
 \description{
-Bind globals used in gen quants or backend
+Combine two sets globals for use in derived quantities or backend
+}
+\seealso{
+\code{\link[=compute_SBC]{compute_SBC()}}, \code{\link[=derived_quantities]{derived_quantities()}}
 }
diff --git a/man/compute_SBC.Rd b/man/compute_SBC.Rd
index 0129322..375a321 100644
--- a/man/compute_SBC.Rd
+++ b/man/compute_SBC.Rd
@@ -12,10 +12,11 @@ compute_SBC(
   thin_ranks = SBC_backend_default_thin_ranks(backend),
   ensure_num_ranks_divisor = 2,
   chunk_size = default_chunk_size(length(datasets)),
-  gen_quants = NULL,
+  dquants = NULL,
   cache_mode = "none",
   cache_location = NULL,
-  globals = list()
+  globals = list(),
+  gen_quants = NULL
 )
 }
 \arguments{
@@ -54,6 +55,8 @@ you can often reduce computation time noticeably by increasing this value.
 You can use \code{options(SBC.min_chunk_size = value)} to set a minimum chunk size globally.
 See documentation of \code{future.chunk.size} argument for \code{\link[future.apply:future_lapply]{future.apply::future_lapply()}} for more details.}
 
+\item{dquants}{Derived quantities to include in SBC. Use \code{\link[=derived_quantities]{derived_quantities()}} to construct them.}
+
 \item{cache_mode}{Type of caching of results, currently the only supported modes are
 \code{"none"} (do not cache) and \code{"results"} where the whole results object is stored
 and recomputed only when the hash of the backend or dataset changes.}
@@ -67,6 +70,8 @@ in the global environment and need to present for the backend to work (
 if they are not already available in package).
 It is added to the \code{globals} argument to \code{\link[future:future]{future::future()}}, to make those
 objects available on all workers.}
+
+\item{gen_quants}{Deprecated, use dquants instead}
 }
 \value{
 An object of class \code{\link[=SBC_results]{SBC_results()}}.
diff --git a/man/compute_dquants.Rd b/man/compute_dquants.Rd
new file mode 100644
index 0000000..bdc0718
--- /dev/null
+++ b/man/compute_dquants.Rd
@@ -0,0 +1,14 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{compute_dquants}
+\alias{compute_dquants}
+\title{Compute derived quantities based on given data and posterior draws.}
+\usage{
+compute_dquants(draws, generated, dquants, gen_quants = NULL)
+}
+\arguments{
+\item{gen_quants}{Deprecated, use \code{dquants}}
+}
+\description{
+Compute derived quantities based on given data and posterior draws.
+}
diff --git a/man/compute_gen_quants-deprecated.Rd b/man/compute_gen_quants-deprecated.Rd
new file mode 100644
index 0000000..0a18110
--- /dev/null
+++ b/man/compute_gen_quants-deprecated.Rd
@@ -0,0 +1,12 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{compute_gen_quants-deprecated}
+\alias{compute_gen_quants-deprecated}
+\title{Compute derived quantities based on given data and posterior draws.}
+\description{
+Delegates directly to \code{compute_dquants()}.
+}
+\seealso{
+\code{\link{SBC-deprecated}}
+}
+\keyword{internal}
diff --git a/man/generated_quantities.Rd b/man/derived_quantities.Rd
similarity index 55%
rename from man/generated_quantities.Rd
rename to man/derived_quantities.Rd
index 812b782..0b51f02 100644
--- a/man/generated_quantities.Rd
+++ b/man/derived_quantities.Rd
@@ -1,10 +1,10 @@
 % Generated by roxygen2: do not edit by hand
-% Please edit documentation in R/results.R
-\name{generated_quantities}
-\alias{generated_quantities}
-\title{Create a definition of generated quantities evaluated in R.}
+% Please edit documentation in R/derived-quantities.R
+\name{derived_quantities}
+\alias{derived_quantities}
+\title{Create a definition of derived quantities evaluated in R.}
 \usage{
-generated_quantities(..., .globals = list())
+derived_quantities(..., .globals = list())
 }
 \arguments{
 \item{...}{named expressions representing the quantitites}
@@ -21,3 +21,16 @@ named in the \code{.globals} parameter (hopefully we'll be able to detect those
 automatically in the future). Note that \code{\link[=recompute_SBC_statistics]{recompute_SBC_statistics()}} currently
 does not use parallel processing, so \code{.globals} don't need to be set.
 }
+\examples{
+# Derived quantity computing the total log likelihood of a normal distribution
+# with known sd = 1
+normal_lpdf <- function(y, mu, sigma) {
+ sum(dnorm(y, mean = mu, sd = sigma, log = TRUE))
+}
+
+# Note the use of .globals to make the normal_lpdf function available
+# within the expression
+log_lik_dq <- derived_quantities(log_lik = normal_lpdf(y, mu, 1),
+                                .globals = "normal_lpdf" )
+
+}
diff --git a/man/generated_quantities-deprecated.Rd b/man/generated_quantities-deprecated.Rd
new file mode 100644
index 0000000..aefcb5b
--- /dev/null
+++ b/man/generated_quantities-deprecated.Rd
@@ -0,0 +1,16 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{generated_quantities-deprecated}
+\alias{generated_quantities-deprecated}
+\title{Create a definition of derived quantities evaluated in R.}
+\description{
+Delegates directly to \code{derived_quantities()}.
+
+Delegates directly to \code{validate_derived_quantities()}.
+}
+\seealso{
+\code{\link{SBC-deprecated}}
+
+\code{\link{SBC-deprecated}}
+}
+\keyword{internal}
diff --git a/man/recompute_SBC_statistics.Rd b/man/recompute_SBC_statistics.Rd
index 203c49b..d4463f8 100644
--- a/man/recompute_SBC_statistics.Rd
+++ b/man/recompute_SBC_statistics.Rd
@@ -10,6 +10,7 @@ recompute_SBC_statistics(
   backend,
   thin_ranks = SBC_backend_default_thin_ranks(backend),
   ensure_num_ranks_divisor = 2,
+  dquants = NULL,
   gen_quants = NULL
 )
 }
@@ -25,11 +26,15 @@ thinned draws See details below.}
 
 \item{ensure_num_ranks_divisor}{Potentially drop some posterior samples to
 ensure that this number divides the total number of SBC ranks (see Details).}
+
+\item{dquants}{Derived quantities to include in SBC. Use \code{\link[=derived_quantities]{derived_quantities()}} to construct them.}
+
+\item{gen_quants}{Deprecated, use dquants instead}
 }
 \value{
 An S3 object of class \code{SBC_results} with updated \verb{$stats} and \verb{$default_diagnostics} fields.
 }
 \description{
 Useful for example to recompute SBC ranks with a different choice of \code{thin_ranks}
-or added generated quantities.
+or added derived quantities.
 }
diff --git a/man/validate_derived_quantities.Rd b/man/validate_derived_quantities.Rd
new file mode 100644
index 0000000..79fac3b
--- /dev/null
+++ b/man/validate_derived_quantities.Rd
@@ -0,0 +1,11 @@
+% Generated by roxygen2: do not edit by hand
+% Please edit documentation in R/derived-quantities.R
+\name{validate_derived_quantities}
+\alias{validate_derived_quantities}
+\title{Validate a definition of derived quantities evaluated in R.}
+\usage{
+validate_derived_quantities(x)
+}
+\description{
+Validate a definition of derived quantities evaluated in R.
+}
diff --git a/tests/testthat/test-results.R b/tests/testthat/test-results.R
index 3fafd3f..9e877c0 100644
--- a/tests/testthat/test-results.R
+++ b/tests/testthat/test-results.R
@@ -166,7 +166,7 @@ test_that("SBC_statistics_from_single_fit", {
     # testing that no error is thrown and structure is OK
     test_draws <- posterior::example_draws(example = "eight_schools")
     res <- SBC_statistics_from_single_fit(test_draws,
-                               variables = vars, thin_ranks = 1, gen_quants = NULL,
+                               variables = vars, thin_ranks = 1, dquants = NULL,
                                ensure_num_ranks_divisor = 1,
                                backend = SBC_backend_mock())
 
@@ -181,7 +181,7 @@ test_that("SBC_statistics_from_single_fit", {
     # Make sure the test draws have the expected size before proceeding
     expect_equal(posterior::ndraws(test_draws), 400)
     res_ensure2 <- SBC_statistics_from_single_fit(posterior::example_draws(example = "eight_schools"),
-                                      variables = vars, thin_ranks = 1, gen_quants = NULL,
+                                      variables = vars, thin_ranks = 1, dquants = NULL,
                                       ensure_num_ranks_divisor = 2,
                                       backend = SBC_backend_mock())
     # Number of ranks = max_rank + 1 (as 0 is a valid rank)
@@ -190,7 +190,7 @@ test_that("SBC_statistics_from_single_fit", {
 
     # Test ensure_num_ranks_divisor, combined with thin_ranks
     res_ensure7 <- SBC_statistics_from_single_fit(posterior::example_draws(example = "eight_schools"),
-                                              variables = vars, thin_ranks = 4, gen_quants = NULL,
+                                              variables = vars, thin_ranks = 4, dquants = NULL,
                                               ensure_num_ranks_divisor = 7,
                                               backend = SBC_backend_mock())
     expect_equal(unique(res_ensure7$max_rank), 97)
diff --git a/vignettes/SBC.Rmd b/vignettes/SBC.Rmd
index 8ebc680..641614b 100644
--- a/vignettes/SBC.Rmd
+++ b/vignettes/SBC.Rmd
@@ -30,7 +30,7 @@ then for each variable, the ranks obtained in SBC should be uniformly distribute
 This corresponds quite directly to claims like 
 "the posterior 84% credible interval should contain the simulated value in 84% of simulations",
 the rank uniformity represents this claim for all interval widths at once. The theory of SBC is fully
-described in [Talts et al.](https://arxiv.org/abs/1804.06788)
+described in [Modrák et al.](https://arxiv.org/abs/2211.02383v1) which builds upon [Talts et al.](https://arxiv.org/abs/1804.06788)
 
 This opens two principal use-cases of SBC:
 
diff --git a/vignettes/brms.Rmd b/vignettes/brms.Rmd
index 79013a6..b241980 100644
--- a/vignettes/brms.Rmd
+++ b/vignettes/brms.Rmd
@@ -180,11 +180,11 @@ n_sims_generator <- SBC_generator_function(one_sim_generator, N = 18, K = 5)
 ```
 
 For increased sensitivity, we also add the log likelihood of the data given parameters
-as a generated quantity that we'll also monitor (see the [`limits_of_SBC`](https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html) 
+as a derived quantity that we'll also monitor (see the [`limits_of_SBC`](https://hyunjimoon.github.io/SBC/articles/limits_of_SBC.html) 
 vignette for discussion on why this is useful).
 
 ```{r}
-log_lik_gq_func <- generated_quantities(
+log_lik_dq_func <- derived_quantities(
   log_lik = sum(dnorm(y, b_Intercept + x * b_x + r_group[group], sigma, log = TRUE))
   # Testing CRPS, probably not worth it
   #, CRPS = mean(scoringRules::crps_norm(y, b_Intercept + x * b_x + r_group[group], sigma))
@@ -218,7 +218,7 @@ So we can happily compute:
 
 ```{r}
 results_func <- compute_SBC(datasets_func, backend_func, 
-                                gen_quants = log_lik_gq_func, 
+                                dquants = log_lik_dq_func, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "func"))
 ```
@@ -262,7 +262,7 @@ Let's fit the same simulations with the new backend.
 
 ```{r}
 results_func2 <- compute_SBC(datasets_func, backend_func2, 
-                                 gen_quants = log_lik_gq_func, 
+                                 dquants = log_lik_dq_func, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "func2"))
 ```
diff --git a/vignettes/discrete_vars.Rmd b/vignettes/discrete_vars.Rmd
index 9a5586c..338627e 100644
--- a/vignettes/discrete_vars.Rmd
+++ b/vignettes/discrete_vars.Rmd
@@ -114,15 +114,15 @@ datasets_1 <- generate_datasets(generator_1, 30)
 ```
 
 Additionally,
-we'll add a generated quantity expressing the total log-likelihood of data given the
-fitted parameters. The expression within the `generated_quantities()` call is evaluated
+we'll add a derived quantity expressing the total log-likelihood of data given the
+fitted parameters. The expression within the `derived_quantities()` call is evaluated
 for both prior and posterior draws and
-included as another variable in SBC checks. It turns out this type of generated quantities
+included as another variable in SBC checks. It turns out this type of derived quantities
 can increase the sensitivity of the SBC against some issues in the model. 
 See `vignette("limits_of_SBC")` for a more detailed discussion of this.
 
 ```{r}
-log_lik_gq <- generated_quantities(log_lik = sum(dpois(y, ifelse(1:T < s, e, l), log = TRUE)))
+log_lik_dq <- derived_quantities(log_lik = sum(dpois(y, ifelse(1:T < s, e, l), log = TRUE)))
 ```
 
 So finally, lets actually compute SBC:
@@ -131,7 +131,7 @@ So finally, lets actually compute SBC:
 results_1 <- compute_SBC(datasets_1, backend_1, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "model1"),
-                    gen_quants = log_lik_gq)
+                    dquants = log_lik_dq)
 ```
 
 Here we also use the caching feature to avoid recomputing the fits when recompiling this vignette. 
@@ -149,7 +149,7 @@ dplyr::filter(results_1$stats, variable == "s")
 
 Inspecting the statistics shows that quite often, the model is quite sure of the value of `s` while the simulated value is just one less. 
 
-Looking at the `ecdf_diff` plot we see that this seems to compromise heavily the inference for `s`, but the other parameters do not show such bad behaviour. Note that the `log_lik` generated quantity shows even starker
+Looking at the `ecdf_diff` plot we see that this seems to compromise heavily the inference for `s`, but the other parameters do not show such bad behaviour. Note that the `log_lik` derived quantity shows even starker
 failure than `s`, so it indeed poses a stricter check in this scenario. 
 
 ```{r results1_plots}
@@ -208,7 +208,7 @@ And we can recompute:
 set.seed(5846502)
 datasets_2 <- generate_datasets(generator_2, 30)
 results_2 <- compute_SBC(datasets_2, backend_1,
-                    gen_quants = log_lik_gq, 
+                    dquants = log_lik_dq, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "model2"))
 ```
@@ -225,7 +225,7 @@ Looks good, so let us add some more simulations to make sure the model behaves w
 set.seed(54321488)
 datasets_2_more <- generate_datasets(generator_2, 100)
 results_2_more <- compute_SBC(datasets_2_more, backend_1,
-                    gen_quants = log_lik_gq, 
+                    dquants = log_lik_dq, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "model3"))
 
@@ -238,7 +238,7 @@ plot_ecdf_diff(results_2_all)
 ```
 
 
-Now - as far as this amount of SBC steps can see, the model is good and we get good behaviour for both the continuous and the discrete parameters and the `log_lik` generated quantity. Hooray!
+Now - as far as this amount of SBC steps can see, the model is good and we get good behaviour for both the continuous and the discrete parameters and the `log_lik` derived quantity. Hooray!
 
 ## JAGS version
 
@@ -276,7 +276,7 @@ data in exactly the same format as Stan, so we can reuse the datasets without an
 ```{r}
 datasets_2_all <- bind_datasets(datasets_2, datasets_2_more)
 results_jags <- compute_SBC(datasets_2_all, backend_jags,
-                            gen_quants = log_lik_gq,
+                            dquants = log_lik_dq,
                         cache_mode = "results",
                         cache_location = file.path(cache_dir_jags, "rjags"))
 ```
@@ -318,7 +318,7 @@ Then we run the actual SBC:
 
 ```{r}
 results_jags_marginalized <- compute_SBC(datasets_2_all, backend_jags_marginalized,
-                                         gen_quants = log_lik_gq,
+                                         dquants = log_lik_dq,
                         cache_mode = "results",
                         cache_location = file.path(cache_dir_jags, "rjags_marginalized"))
 ```
diff --git a/vignettes/limits_of_SBC.Rmd b/vignettes/limits_of_SBC.Rmd
index 4980155..e3048a9 100644
--- a/vignettes/limits_of_SBC.Rmd
+++ b/vignettes/limits_of_SBC.Rmd
@@ -11,12 +11,14 @@ vignette: >
   \usepackage[utf8]{inputenc}
 ---
 
-Here, we'll walk through some problems that are hard/impossible to diagnose with SBC.
+Here, we'll walk through some problems that are hard to diagnose with SBC in its default settings.
 As usual the focus is on problems with models, assuming our inference algorithm 
 is correct. But for each of those problems, one can imagine a corresponding
 failure in an algorithm --- although some of those failures are quite unlikely for
 actual algorithms.
 
+A more extensive theoretical discussion of those limits can be found in the [Simulation-Based Calibration Checking for Bayesian Computation: The Choice of Test Quantities Shapes Sensitivity](https://arxiv.org/abs/2211.02383v1) preprint, additional examples at https://martinmodrak.github.io/sbc_test_quantities_paper/
+
 ```{r setup, message=FALSE,warning=FALSE, results="hide"}
 library(SBC)
 library(ggplot2)
@@ -306,7 +308,7 @@ plot_sim_estimated(results_missing, alpha = 0.5)
 
 
 There is however even more powerful method - and that is to include the likelihood in the SBC.
-This is most easily done by adding a "generated quantity" to the SBC results - this is a function
+This is most easily done by adding a "derived quantity" to the SBC results - this is a function
 that is evaluated within the context of the variables AND data. 
 And it can be added without recomputing the fits!
 
@@ -315,19 +317,19 @@ normal_lpdf <- function(y, mu, sigma) {
   sum(dnorm(y, mean = mu, sd = sigma, log = TRUE))
 }
 
-log_lik_gq <- generated_quantities(log_lik = normal_lpdf(y, mu, 1), 
+log_lik_dq <- derived_quantities(log_lik = normal_lpdf(y, mu, 1), 
                                    .globals = "normal_lpdf" )
 
-results_missing_gq <- recompute_SBC_statistics(
+results_missing_dq <- recompute_SBC_statistics(
   results_missing, datasets_missing, 
-  backend = backend_missing, gen_quants = log_lik_gq)
+  backend = backend_missing, dquants = log_lik_dq)
 ```
 
 The rank plots for the `log_lik` quantity immediately shows a severe problem:
 
-```{r results_missing_gq_plots}
-plot_ecdf_diff(results_missing_gq)
-plot_rank_hist(results_missing_gq)
+```{r results_missing_dq_plots}
+plot_ecdf_diff(results_missing_dq)
+plot_rank_hist(results_missing_dq)
 ```
 
 
@@ -359,7 +361,7 @@ if(use_cmdstanr) {
 Let us use this model for the same set of simulations.
 
 ```{r}
-results_missing_2 <- compute_SBC(datasets_missing, backend_missing_2, gen_quants = log_lik_gq, 
+results_missing_2 <- compute_SBC(datasets_missing, backend_missing_2, dquants = log_lik_dq, 
                     cache_mode = "results", 
                     cache_location = file.path(cache_dir, "missing_2"))
 ```
@@ -377,7 +379,7 @@ plot_sim_estimated(results_missing_2, variables = "mu", alpha = 0.5)
 ```
 
 
-Now contraction is pretty high, and `mu` is behaving well, but our `log_lik` generated quantity shows a clear problem
+Now contraction is pretty high, and `mu` is behaving well, but our `log_lik` derived quantity shows a clear problem
 
 ```{r results_missing_2_plots}
 plot_ecdf_diff(results_missing_2)
@@ -470,17 +472,17 @@ We can however add derived quantities that depend on both elements of mu. We'll
 try their sum, difference, product and the multivarite normal log likelihood
 
 ```{r}
-gq_corr <- generated_quantities(sum = mu[1] + mu[2], 
+dq_corr <- derived_quantities(sum = mu[1] + mu[2], 
                                 diff = mu[1] - mu[2],
                                 prod = mu[1] * mu[2],
                                 mvn_log_lik = sum(mvtnorm::dmvnorm(y, mean = mu, sigma = mvn_sigma, log = TRUE)))
 
 
-res_corr_gq  <- compute_SBC(datasets_correlated, backend_uncorr, keep_fits = FALSE,
+res_corr_dq  <- compute_SBC(datasets_correlated, backend_uncorr, keep_fits = FALSE,
                         globals = analytic_backend_uncorr_globals,
-                        gen_quants = gq_corr,
+                        dquants = dq_corr,
                         cache_mode = "results", 
-                        cache_location = file.path(cache_dir, "corr_gq"))
+                        cache_location = file.path(cache_dir, "corr_dq"))
 
 ```
 
@@ -488,7 +490,7 @@ We see that all of the derived quantities show problems, but with different stre
 of signal. We'll especially note that the log likelihood is once again a very good
 choice, while sum is probably the worst of those tested.
 
-```{r results_corr_gq}
-plot_rank_hist(res_corr_gq)
-plot_ecdf_diff(res_corr_gq)
+```{r results_corr_dq}
+plot_rank_hist(res_corr_dq)
+plot_ecdf_diff(res_corr_dq)
 ```
diff --git a/vignettes/overview_wide.graphml b/vignettes/overview_wide.graphml
index d72b0d1..1df7ffd 100644
--- a/vignettes/overview_wide.graphml
+++ b/vignettes/overview_wide.graphml
@@ -1,6 +1,6 @@
 <?xml version="1.0" encoding="UTF-8" standalone="no"?>
 <graphml xmlns="http://graphml.graphdrawing.org/xmlns" xmlns:java="http://www.yworks.com/xml/yfiles-common/1.0/java" xmlns:sys="http://www.yworks.com/xml/yfiles-common/markup/primitives/2.0" xmlns:x="http://www.yworks.com/xml/yfiles-common/markup/2.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:y="http://www.yworks.com/xml/graphml" xmlns:yed="http://www.yworks.com/xml/yed/3" xsi:schemaLocation="http://graphml.graphdrawing.org/xmlns http://www.yworks.com/xml/schema/graphml/1.1/ygraphml.xsd">
-  <!--Created by yEd 3.21.1-->
+  <!--Created by yEd 3.19.1.1-->
   <key attr.name="Description" attr.type="string" for="graph" id="d0"/>
   <key for="port" id="d1" yfiles.type="portgraphics"/>
   <key for="port" id="d2" yfiles.type="portgeometry"/>
@@ -257,7 +257,7 @@ data<y:LabelModel><y:SmartNodeLabelModel distance="4.0"/></y:LabelModel><y:Model
           <y:Geometry height="30.0" width="114.0" x="924.021484375" y="-115.87353515625"/>
           <y:Fill color="#FFCC99" transparent="false"/>
           <y:BorderStyle color="#000000" raised="false" type="line" width="1.0"/>
-          <y:NodeLabel alignment="center" autoSizePolicy="content" fontFamily="Dialog" fontSize="12" fontStyle="plain" hasBackgroundColor="false" hasLineColor="false" height="18.701171875" horizontalTextPosition="center" iconTextGap="4" modelName="custom" textColor="#000000" verticalTextPosition="bottom" visible="true" width="92.04296875" x="10.978515625" xml:space="preserve" y="5.6494140625">compute_results<y:LabelModel><y:SmartNodeLabelModel distance="4.0"/></y:LabelModel><y:ModelParameter><y:SmartNodeLabelModelParameter labelRatioX="0.0" labelRatioY="0.0" nodeRatioX="0.0" nodeRatioY="0.0" offsetX="0.0" offsetY="0.0" upX="0.0" upY="-1.0"/></y:ModelParameter></y:NodeLabel>
+          <y:NodeLabel alignment="center" autoSizePolicy="content" fontFamily="Dialog" fontSize="12" fontStyle="plain" hasBackgroundColor="false" hasLineColor="false" height="18.701171875" horizontalTextPosition="center" iconTextGap="4" modelName="custom" textColor="#000000" verticalTextPosition="bottom" visible="true" width="81.373046875" x="16.3134765625" xml:space="preserve" y="5.6494140625">compute_SBC<y:LabelModel><y:SmartNodeLabelModel distance="4.0"/></y:LabelModel><y:ModelParameter><y:SmartNodeLabelModelParameter labelRatioX="0.0" labelRatioY="0.0" nodeRatioX="0.0" nodeRatioY="0.0" offsetX="0.0" offsetY="0.0" upX="0.0" upY="-1.0"/></y:ModelParameter></y:NodeLabel>
           <y:Shape type="rectangle"/>
         </y:ShapeNode>
       </data>
diff --git a/vignettes/overview_wide.png b/vignettes/overview_wide.png
index ec8847c..c95fbb0 100644
Binary files a/vignettes/overview_wide.png and b/vignettes/overview_wide.png differ
diff --git a/vignettes/rejection_sampling.Rmd b/vignettes/rejection_sampling.Rmd
index 6a2f9a8..e46f7c9 100644
--- a/vignettes/rejection_sampling.Rmd
+++ b/vignettes/rejection_sampling.Rmd
@@ -27,13 +27,8 @@ simulation and only accept it when it passes a certain condition we impose
 (e.g. that no observed count is larger than $10^8$).
 But does rejection sampling when generating simulations affect the validity of SBC?
 
-Thanks to forum user Niko Huurre who derived the necessary math
-at [Stan Discourse discussion of the topic](https://discourse.mc-stan.org/t/using-narrower-priors-for-sbc/21709/6?u=martinmodrak)
-we know exactly when it is OK. Briefly: for algorithms
-that only need to know the posterior density up to a constant (which includes Stan
-and many others),
-it is OK as long as the rejection criterion only
-uses observed data and not the unobserved variables.
+It turns out that it does not as long as the rejection criterion only
+uses observed data and not the unobserved variables. 
 
 We'll first walk through the math and then show examples of both OK and problematic
 rejection sampling.
@@ -41,47 +36,20 @@ rejection sampling.
 
 ## The math
 
-Let $f\left(y\right)$ be the probability that the simulated data $y$ is rejected (usually a 0-1 function if you have a clear idea what a "bad" dataset looks like, but could be probabilistic if you're relying on finicky diagnostics). The important numbers are the probability of rejection for variable $\theta$
+Let $\mathtt{accept}(y)$ be the probability the the simulated data $y$ is accepted. Note that $\mathtt{accept}$  uses only data as input and would usually be a 0-1 function if you have a clear idea what a "bad" dataset looks like, but could be probabilistic if you're relying on finicky diagnostics. 
 
-$$
-L\left(\theta\right)=\int f\left(y\right)\pi\left(y|\theta\right)\mathrm{d}y
-$$
-
-and the total rate of rejections from the prior
-
-$$
-R=\iint f\left(y\right)\pi\left(y|\theta\right)\pi\left(\theta\right)\mathrm{d}y\mathrm{d}\theta=\int L\left(\theta\right)\pi\left(\theta\right)\mathrm{d}\theta
-$$
-
-Rejecting the simulation when it generates “bad” data effectively distorts the prior
-
-$$
-\pi\left(\theta\right)\to\frac{L\left(\theta\right)}{R}\pi\left(\theta\right)
-$$
-
-and of course rejections change the generating distribution
+We define a variable $a \sim \text{Bernoulli}(\mathtt{accept}(y))$. Given the parameter space $\Theta$ and a specific $\theta \in \Theta$, this implies a joint distribution $\pi(\theta, y, a)$ that factorizes as $\pi(\theta, y, a) = \pi(a|y)\pi(y | \theta)\pi(\theta)$. We can then look at the posterior conditional on accepting a dataset to see the claimed invariance:
 
 $$
-\pi\left(y|\theta\right)\to\frac{f\left(y\right)}{L\left(\theta\right)}\pi\left(y|\theta\right)
+\begin{equation}
+\pi(\theta | y, a = 1) = \frac{\pi(a = 1 | y) \pi(y | \theta)\pi(\theta)}{\int_\Theta \mathrm{d}\tilde\theta \: \pi(a = 1 | y) \pi(y | \tilde\theta)\pi(\tilde\theta)} = 
+\frac{\pi(y | \theta)\pi(\theta)}{\int_\Theta \mathrm{d}\tilde\theta \: \pi(y | \tilde\theta)\pi(\tilde\theta)} = \pi(\theta | y)
+\end{equation}
 $$
 
-but crucially these changes cancel out when computing the posterior. Before rejections we have:
-
-$$
-\pi(\theta | y) \propto \pi(y | \theta) \pi(\theta)
-$$
-
-After rejections we have
-
-$$
-\pi(\theta | y) \propto \frac{L(\theta)}{R} \pi(y | \theta) \frac{f(y)}{L(\theta)} \pi(\theta) = \frac{f(y)}{R} \pi(y | \theta) \pi(\theta)
-$$
 
-And since $\frac{f(y)}{R}$ is a constant for any given simulation (and hence the fit), 
-the overall posterior for Stan (and most other MCMC algorithms) is the same, 
-because Stan only needs the posterior density up to a constant. 
 So whether we take rejection into account or not, the model will match the generating process. 
-However, if $f$ also depended on $\theta$, it would no longer contribute a constant
+However, if $\mathtt{accept}$ also depended on $\theta$, it would no longer contribute a constant
 and we'll get a mismatch between the generator and model.
 
 ## Practical examples