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MCMCDiagnosticTools

MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.

Background

Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.

Effective sample size and $\widehat{R}$

MCMCDiagnosticTools.ess — Function
ess(
+Home · MCMCDiagnosticTools.jl
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GitHub
MCMCDiagnosticTools
MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
Background
Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Function
ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
source
MCMCDiagnosticTools.rafterydiag — Function
rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.

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-Home · MCMCDiagnosticTools.jl
Edit on GitHub
MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Function
ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
Edit on GitHub
MCMCDiagnosticTools
Effective sample size and $\widehat{R}$
MCMCDiagnosticTools.ess — Function
ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
kwargs are forwarded to mcse.
source
MCMCDiagnosticTools.rafterydiag — Function
rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
source
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.

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diff --git a/previews/PR100/search/index.html b/previews/PR100/search/index.html
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--- a/previews/PR100/search/index.html
+++ b/previews/PR100/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
Loading search...
    
+Search · MCMCDiagnosticTools.jl
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diff --git a/previews/PR101/index.html b/previews/PR101/index.html
index ed718741..6956c2e9 100644
--- a/previews/PR101/index.html
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@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
      Edit on GitHub
      MCMCDiagnosticTools
      Effective sample size and $\widehat{R}$
      MCMCDiagnosticTools.ess — Function
      ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
      Edit on GitHub
      MCMCDiagnosticTools
      Effective sample size and $\widehat{R}$
      MCMCDiagnosticTools.ess — Function
      ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
      kwargs are forwarded to mcse.
      source
      MCMCDiagnosticTools.rafterydiag — Function
      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
      source
      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
      • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
      • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
      
+
diff --git a/previews/PR101/search/index.html b/previews/PR101/search/index.html
index 3c694d2f..7167095d 100644
--- a/previews/PR101/search/index.html
+++ b/previews/PR101/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
      Loading search...
        
+Search · MCMCDiagnosticTools.jl
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diff --git a/previews/PR98/index.html b/previews/PR98/index.html
index ee42d012..c012de19 100644
--- a/previews/PR98/index.html
+++ b/previews/PR98/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
          Edit on GitHub
          MCMCDiagnosticTools
          Effective sample size and $\widehat{R}$
          MCMCDiagnosticTools.ess — Function
          ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
          Edit on GitHub
          MCMCDiagnosticTools
          Effective sample size and $\widehat{R}$
          MCMCDiagnosticTools.ess — Function
          ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
          Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
          kwargs are forwarded to mcse.
          source
          MCMCDiagnosticTools.rafterydiag — Function
          rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
          Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
          Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
          source
          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
          • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
          • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
          • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
          • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
          • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
          • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
          • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
          • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
          • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
          • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
          • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
          
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diff --git a/previews/PR98/search/index.html b/previews/PR98/search/index.html
index d4586001..fa0e95e9 100644
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+++ b/previews/PR98/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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index fd16ce7f..8b5db82a 100644
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+++ b/previews/PR99/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
              Edit on GitHub
              MCMCDiagnosticTools
              Effective sample size and $\widehat{R}$
              MCMCDiagnosticTools.ess — Function
              ess(
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              MCMCDiagnosticTools
              Effective sample size and $\widehat{R}$
              MCMCDiagnosticTools.ess — Function
              ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
              Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
              kwargs are forwarded to mcse.
              source
              MCMCDiagnosticTools.rafterydiag — Function
              rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
              Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
              Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
              source
              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
              • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
              • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
              • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
              • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
              • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
              • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
              • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
              • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
              • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
              • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
              • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
              
+
diff --git a/previews/PR99/search/index.html b/previews/PR99/search/index.html
index 060c6780..6b80fc06 100644
--- a/previews/PR99/search/index.html
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@@ -1,2 +1,458 @@
 
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index 03eb8385..e4f358c8 100644
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+++ b/v0.1.0/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                  Edit on GitHub
                  MCMCDiagnosticTools
                  Effective sample size and potential scale reduction
                  The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                  MCMCDiagnosticTools.ess_rhat — Function
                  ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                  Edit on GitHub
                  MCMCDiagnosticTools
                  Effective sample size and potential scale reduction
                  The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                  MCMCDiagnosticTools.ess_rhat — Function
                  ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                  Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                  See also: ESSMethod, FFTESSMethod, BDAESSMethod
                  source
                  The following methods are supported:
                  MCMCDiagnosticTools.ESSMethod — Type
                  ESSMethod <: AbstractESSMethod
                  The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                  It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                  References
                  Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                  Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                  source
                  MCMCDiagnosticTools.FFTESSMethod — Type
                  FFTESSMethod <: AbstractESSMethod
                  The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                  The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                  Info
                  To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                  source
                  MCMCDiagnosticTools.BDAESSMethod — Type
                  BDAESSMethod <: AbstractESSMethod
                  The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                  It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                  References
                  Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                  Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                  source
                  Monte Carlo standard error
                  MCMCDiagnosticTools.mcse — Function
                  mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                  Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                  source
                  R⋆ diagnostic
                  MCMCDiagnosticTools.rstar — Function
                  rstar(
     rng=Random.GLOBAL_RNG,
@@ -23,3 +478,4 @@
 true
                  References
                  Lambert, B., & Vehtari, A. (2020). $R^*$: A robust MCMC convergence diagnostic with uncertainty using decision tree classifiers.
                  source
                  Other diagnostics
                  MCMCDiagnosticTools.discretediag — Function
                  discretediag(chains::AbstractArray{<:Real,3}; frac=0.3, method=:weiss, nsim=1_000)
                  Compute discrete diagnostic where method can be one of :weiss, :hangartner, :DARBOOT, :MCBOOT, :billinsgley, and :billingsleyBOOT.
                  source
                  MCMCDiagnosticTools.gewekediag — Function
                  gewekediag(x::AbstractVector{<:Real}; first::Real=0.1, last::Real=0.5, kwargs...)
                  Compute the Geweke diagnostic from the first and last proportion of samples x.
                  source
                  MCMCDiagnosticTools.heideldiag — Function
                  heideldiag(
     x::AbstractVector{<:Real}; alpha::Real=0.05, eps::Real=0.1, start::Int=1, kwargs...
 )
                  Compute the Heidelberger and Welch diagnostic.
                  source
                  • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                  
+
diff --git a/v0.1.0/search/index.html b/v0.1.0/search/index.html
index fcc3dab3..008f6364 100644
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@@ -1,2 +1,458 @@
 
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@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                      Edit on GitHub
                      MCMCDiagnosticTools
                      Effective sample size and potential scale reduction
                      The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                      MCMCDiagnosticTools.ess_rhat — Function
                      ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                      Edit on GitHub
                      MCMCDiagnosticTools
                      Effective sample size and potential scale reduction
                      The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                      MCMCDiagnosticTools.ess_rhat — Function
                      ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                      Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                      See also: ESSMethod, FFTESSMethod, BDAESSMethod
                      source
                      The following methods are supported:
                      MCMCDiagnosticTools.ESSMethod — Type
                      ESSMethod <: AbstractESSMethod
                      The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                      It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                      References
                      Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                      Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                      source
                      MCMCDiagnosticTools.FFTESSMethod — Type
                      FFTESSMethod <: AbstractESSMethod
                      The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                      The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                      Info
                      To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                      source
                      MCMCDiagnosticTools.BDAESSMethod — Type
                      BDAESSMethod <: AbstractESSMethod
                      The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                      It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                      References
                      Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                      Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                      source
                      Monte Carlo standard error
                      MCMCDiagnosticTools.mcse — Function
                      mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                      Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                      source
                      R⋆ diagnostic
                      MCMCDiagnosticTools.rstar — Function
                      rstar(
     rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
 )
                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                      source
                      MCMCDiagnosticTools.rafterydiag — Function
                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                      source
                      • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                      
+
diff --git a/v0.1.1/search/index.html b/v0.1.1/search/index.html
index db961735..ba1656a4 100644
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index 0cef1c29..2d466116 100644
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@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
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                          MCMCDiagnosticTools
                          Effective sample size and potential scale reduction
                          The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                          MCMCDiagnosticTools.ess_rhat — Function
                          ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                          Edit on GitHub
                          MCMCDiagnosticTools
                          Effective sample size and potential scale reduction
                          The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                          MCMCDiagnosticTools.ess_rhat — Function
                          ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                          Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                          See also: ESSMethod, FFTESSMethod, BDAESSMethod
                          source
                          The following methods are supported:
                          MCMCDiagnosticTools.ESSMethod — Type
                          ESSMethod <: AbstractESSMethod
                          The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                          It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                          References
                          Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                          Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                          source
                          MCMCDiagnosticTools.FFTESSMethod — Type
                          FFTESSMethod <: AbstractESSMethod
                          The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                          The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                          Info
                          To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                          source
                          MCMCDiagnosticTools.BDAESSMethod — Type
                          BDAESSMethod <: AbstractESSMethod
                          The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                          It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                          References
                          Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                          Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                          source
                          Monte Carlo standard error
                          MCMCDiagnosticTools.mcse — Function
                          mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                          Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                          source
                          R⋆ diagnostic
                          MCMCDiagnosticTools.rstar — Function
                          rstar(
     rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
 )
                          Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                          source
                          MCMCDiagnosticTools.rafterydiag — Function
                          rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                          Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                          Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                          source
                          • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                          • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                          • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                          • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                          • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                          • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                          • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                          
+
diff --git a/v0.1.2/search/index.html b/v0.1.2/search/index.html
index fbda25cb..2646b353 100644
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@@ -1,2 +1,458 @@
 
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-Home · MCMCDiagnosticTools.jl
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                              MCMCDiagnosticTools
                              Effective sample size and potential scale reduction
                              The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                              MCMCDiagnosticTools.ess_rhat — Function
                              ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                              Edit on GitHub
                              MCMCDiagnosticTools
                              Effective sample size and potential scale reduction
                              The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                              MCMCDiagnosticTools.ess_rhat — Function
                              ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                              Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                              See also: ESSMethod, FFTESSMethod, BDAESSMethod
                              source
                              The following methods are supported:
                              MCMCDiagnosticTools.ESSMethod — Type
                              ESSMethod <: AbstractESSMethod
                              The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                              It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                              References
                              Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                              Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                              source
                              MCMCDiagnosticTools.FFTESSMethod — Type
                              FFTESSMethod <: AbstractESSMethod
                              The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                              The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                              Info
                              To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                              source
                              MCMCDiagnosticTools.BDAESSMethod — Type
                              BDAESSMethod <: AbstractESSMethod
                              The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                              It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                              References
                              Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                              Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                              source
                              Monte Carlo standard error
                              MCMCDiagnosticTools.mcse — Function
                              mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                              Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                              source
                              R⋆ diagnostic
                              MCMCDiagnosticTools.rstar — Function
                              rstar(
     rng=Random.GLOBAL_RNG,
@@ -25,3 +480,4 @@
 )
                              Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                              source
                              MCMCDiagnosticTools.rafterydiag — Function
                              rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                              Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                              Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                              source
                              • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                              • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                              • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                              • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                              • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                              • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                              • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                              
+
diff --git a/v0.1.3/search/index.html b/v0.1.3/search/index.html
index efaa66e2..16f1001e 100644
--- a/v0.1.3/search/index.html
+++ b/v0.1.3/search/index.html
@@ -1,2 +1,458 @@
 
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@@ -1,5 +1,460 @@
 
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                                  MCMCDiagnosticTools
                                  Effective sample size and potential scale reduction
                                  The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                  MCMCDiagnosticTools.ess_rhat — Function
                                  ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                                  Edit on GitHub
                                  MCMCDiagnosticTools
                                  Effective sample size and potential scale reduction
                                  The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                  MCMCDiagnosticTools.ess_rhat — Function
                                  ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                                  Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                                  See also: ESSMethod, FFTESSMethod, BDAESSMethod
                                  source
                                  The following methods are supported:
                                  MCMCDiagnosticTools.ESSMethod — Type
                                  ESSMethod <: AbstractESSMethod
                                  The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                  It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                                  References
                                  Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                  Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                  source
                                  MCMCDiagnosticTools.FFTESSMethod — Type
                                  FFTESSMethod <: AbstractESSMethod
                                  The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                  The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                                  Info
                                  To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                                  source
                                  MCMCDiagnosticTools.BDAESSMethod — Type
                                  BDAESSMethod <: AbstractESSMethod
                                  The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                  It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                                  References
                                  Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                  Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                  source
                                  Monte Carlo standard error
                                  MCMCDiagnosticTools.mcse — Function
                                  mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                                  Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                                  source
                                  R⋆ diagnostic
                                  MCMCDiagnosticTools.rstar — Function
                                  rstar(
     rng=Random.GLOBAL_RNG,
@@ -26,3 +481,4 @@
 )
                                  Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                  source
                                  MCMCDiagnosticTools.rafterydiag — Function
                                  rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                  Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                  Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                  source
                                  • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                  
+
diff --git a/v0.1.4/search/index.html b/v0.1.4/search/index.html
index d46338f2..81fafc60 100644
--- a/v0.1.4/search/index.html
+++ b/v0.1.4/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                      Edit on GitHub
                                      MCMCDiagnosticTools
                                      Effective sample size and potential scale reduction
                                      The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                      MCMCDiagnosticTools.ess_rhat — Function
                                      ess_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
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                                      Edit on GitHub
                                      MCMCDiagnosticTools
                                      Effective sample size and potential scale reduction
                                      The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                      MCMCDiagnosticTools.ess_rhat — Function
                                      ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                                      Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, parameters, chains) with the method and a maximum lag of maxlag.
                                      See also: ESSMethod, FFTESSMethod, BDAESSMethod
                                      source
                                      The following methods are supported:
                                      MCMCDiagnosticTools.ESSMethod — Type
                                      ESSMethod <: AbstractESSMethod
                                      The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                      It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                                      References
                                      Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                      Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                      source
                                      MCMCDiagnosticTools.FFTESSMethod — Type
                                      FFTESSMethod <: AbstractESSMethod
                                      The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                      The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                                      Info
                                      To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                                      source
                                      MCMCDiagnosticTools.BDAESSMethod — Type
                                      BDAESSMethod <: AbstractESSMethod
                                      The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                      It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                                      References
                                      Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                      Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                      source
                                      Monte Carlo standard error
                                      MCMCDiagnosticTools.mcse — Function
                                      mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                                      Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                                      source
                                      R⋆ diagnostic
                                      MCMCDiagnosticTools.rstar — Function
                                      rstar(
     rng=Random.GLOBAL_RNG,
@@ -26,3 +481,4 @@
 )
                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                      source
                                      MCMCDiagnosticTools.rafterydiag — Function
                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                      source
                                      • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                      
+
diff --git a/v0.1.5/search/index.html b/v0.1.5/search/index.html
index e49c2ac5..85278911 100644
--- a/v0.1.5/search/index.html
+++ b/v0.1.5/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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index db107d95..c5c1d6f4 100644
--- a/v0.2.0/index.html
+++ b/v0.2.0/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                          Edit on GitHub
                                          MCMCDiagnosticTools
                                          Effective sample size and potential scale reduction
                                          The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                          MCMCDiagnosticTools.ess_rhat — Function
                                          ess_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
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                                          Edit on GitHub
                                          MCMCDiagnosticTools
                                          Effective sample size and potential scale reduction
                                          The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                          MCMCDiagnosticTools.ess_rhat — Function
                                          ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                                          Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, chains, parameters) with the method and a maximum lag of maxlag.
                                          See also: ESSMethod, FFTESSMethod, BDAESSMethod
                                          source
                                          The following methods are supported:
                                          MCMCDiagnosticTools.ESSMethod — Type
                                          ESSMethod <: AbstractESSMethod
                                          The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                          It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                                          References
                                          Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                          Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                          source
                                          MCMCDiagnosticTools.FFTESSMethod — Type
                                          FFTESSMethod <: AbstractESSMethod
                                          The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                          The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                                          Info
                                          To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                                          source
                                          MCMCDiagnosticTools.BDAESSMethod — Type
                                          BDAESSMethod <: AbstractESSMethod
                                          The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                          It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                                          References
                                          Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                          Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                          source
                                          Monte Carlo standard error
                                          MCMCDiagnosticTools.mcse — Function
                                          mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                                          Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                                          source
                                          R⋆ diagnostic
                                          MCMCDiagnosticTools.rstar — Function
                                          rstar(
     rng::Random.AbstractRNG=Random.default_rng(),
@@ -30,3 +485,4 @@
 )
                                          Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                          source
                                          MCMCDiagnosticTools.rafterydiag — Function
                                          rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                          Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                          Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                          source
                                          • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                          • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                          • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                          • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                          • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                          • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                          • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                          • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                          • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                          
+
diff --git a/v0.2.0/search/index.html b/v0.2.0/search/index.html
index 6501c915..555304c3 100644
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+++ b/v0.2.0/search/index.html
@@ -1,2 +1,458 @@
 
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index f1ddc958..db7163cb 100644
--- a/v0.2.1/index.html
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                                              MCMCDiagnosticTools
                                              Effective sample size and potential scale reduction
                                              The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                              MCMCDiagnosticTools.ess_rhat — Function
                                              ess_rhat(
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                                              MCMCDiagnosticTools
                                              Effective sample size and potential scale reduction
                                              The effective sample size (ESS) and the potential scale reduction can be estimated with ess_rhat.
                                              MCMCDiagnosticTools.ess_rhat — Function
                                              ess_rhat(
     samples::AbstractArray{<:Union{Missing,Real},3}; method=ESSMethod(), maxlag=250
 )
                                              Estimate the effective sample size and the potential scale reduction of the samples of shape (draws, chains, parameters) with the method and a maximum lag of maxlag.
                                              See also: ESSMethod, FFTESSMethod, BDAESSMethod
                                              source
                                              The following methods are supported:
                                              MCMCDiagnosticTools.ESSMethod — Type
                                              ESSMethod <: AbstractESSMethod
                                              The ESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                              It is is based on the discussion by Vehtari et al. and uses the biased estimator of the autocovariance, as discussed by Geyer. In contrast to Geyer, the divisor n - 1 is used in the estimation of the autocovariance to obtain the unbiased estimator of the variance for lag 0.
                                              References
                                              Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                              Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                              source
                                              MCMCDiagnosticTools.FFTESSMethod — Type
                                              FFTESSMethod <: AbstractESSMethod
                                              The FFTESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                              The algorithm is the same as the one of ESSMethod but this method uses fast Fourier transforms (FFTs) for estimating the autocorrelation.
                                              Info
                                              To be able to use this method, you have to load a package that implements the AbstractFFTs.jl interface such as FFTW.jl or FastTransforms.jl.
                                              source
                                              MCMCDiagnosticTools.BDAESSMethod — Type
                                              BDAESSMethod <: AbstractESSMethod
                                              The BDAESSMethod uses a standard algorithm for estimating the effective sample size of MCMC chains.
                                              It is is based on the discussion by Vehtari et al. and uses the variogram estimator of the autocorrelation function discussed by Gelman et al.
                                              References
                                              Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                              Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis.
                                              source
                                              Monte Carlo standard error
                                              MCMCDiagnosticTools.mcse — Function
                                              mcse(x::AbstractVector{<:Real}; method::Symbol=:imse, kwargs...)
                                              Compute the Monte Carlo standard error (MCSE) of samples x. The optional argument method describes how the errors are estimated. Possible options are:
                                              source
                                              R⋆ diagnostic
                                              MCMCDiagnosticTools.rstar — Function
                                              rstar(
     rng::Random.AbstractRNG=Random.default_rng(),
@@ -32,3 +487,4 @@
 )
                                              Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                              source
                                              MCMCDiagnosticTools.rafterydiag — Function
                                              rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                              Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                              Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                              source
                                              • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                              • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                              • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                              • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                              • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                              • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                              • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                              • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                              • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                              
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diff --git a/v0.2.1/search/index.html b/v0.2.1/search/index.html
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--- a/v0.2.1/search/index.html
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@@ -1,2 +1,458 @@
 
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                                                  MCMCDiagnosticTools
                                                  Effective sample size and $\widehat{R}$
                                                  The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
                                                  MCMCDiagnosticTools.ess_rhat — Function
                                                  ess_rhat(
+Home · MCMCDiagnosticTools.jl
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                                                  Edit on GitHub
                                                  MCMCDiagnosticTools
                                                  Effective sample size and $\widehat{R}$
                                                  The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
                                                  MCMCDiagnosticTools.ess_rhat — Function
                                                  ess_rhat(
     [estimator,]
     samples::AbstractArray{<:Union{Missing,Real},3};
     method=ESSMethod(),
@@ -36,3 +491,4 @@
 )
                                                  Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                  source
                                                  MCMCDiagnosticTools.rafterydiag — Function
                                                  rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                  Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                  Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                  source
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                  • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                  
+
diff --git a/v0.2.2/search/index.html b/v0.2.2/search/index.html
index 0ae117ae..ca8b4880 100644
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+++ b/v0.2.2/search/index.html
@@ -1,2 +1,458 @@
 
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@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                      Edit on GitHub
                                                      MCMCDiagnosticTools
                                                      Effective sample size and $\widehat{R}$
                                                      The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
                                                      MCMCDiagnosticTools.ess_rhat — Function
                                                      ess_rhat(
+Home · MCMCDiagnosticTools.jl
+
+
+
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                                                      Edit on GitHub
                                                      MCMCDiagnosticTools
                                                      Effective sample size and $\widehat{R}$
                                                      The effective sample size (ESS) and $\widehat{R}$ can be estimated with ess_rhat.
                                                      MCMCDiagnosticTools.ess_rhat — Function
                                                      ess_rhat(
     [estimator,]
     samples::AbstractArray{<:Union{Missing,Real},3};
     method=ESSMethod(),
@@ -36,3 +491,4 @@
 )
                                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                      source
                                                      MCMCDiagnosticTools.rafterydiag — Function
                                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                      source
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                      • Glynn1991Glynn, P. W., & Whitt, W. (1991). Estimating the asymptotic variance with batch means. Operations Research Letters, 10(8), 431-435.
                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                      
+
diff --git a/v0.2.3/search/index.html b/v0.2.3/search/index.html
index be432d77..af9a2b9f 100644
--- a/v0.2.3/search/index.html
+++ b/v0.2.3/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.0/index.html b/v0.3.0/index.html
index 79cb87dd..056ed6ca 100644
--- a/v0.3.0/index.html
+++ b/v0.3.0/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                          Edit on GitHub
                                                          MCMCDiagnosticTools
                                                          Effective sample size and $\widehat{R}$
                                                          MCMCDiagnosticTools.ess — Function
                                                          ess(
+Home · MCMCDiagnosticTools.jl
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                                                          Edit on GitHub
                                                          MCMCDiagnosticTools
                                                          Effective sample size and $\widehat{R}$
                                                          MCMCDiagnosticTools.ess — Function
                                                          ess(
     samples::AbstractArray{<:Union{Missing,Real},3};
     kind=:bulk,
     autocov_method=AutocovMethod(),
@@ -55,3 +510,4 @@
 )
                                                          Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                          kwargs are forwarded to mcse.
                                                          source
                                                          MCMCDiagnosticTools.rafterydiag — Function
                                                          rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                          Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                          Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                          source
                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                          • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                          • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                          • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                          • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                          • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                          • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                          • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                          • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                          • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                          • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                          • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                          
+
diff --git a/v0.3.0/search/index.html b/v0.3.0/search/index.html
index fbf67578..b6ed8a58 100644
--- a/v0.3.0/search/index.html
+++ b/v0.3.0/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.1/index.html b/v0.3.1/index.html
index 8f4ca0f3..3a967be4 100644
--- a/v0.3.1/index.html
+++ b/v0.3.1/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                              Edit on GitHub
                                                              MCMCDiagnosticTools
                                                              Effective sample size and $\widehat{R}$
                                                              MCMCDiagnosticTools.ess — Function
                                                              ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                              Edit on GitHub
                                                              MCMCDiagnosticTools
                                                              Effective sample size and $\widehat{R}$
                                                              MCMCDiagnosticTools.ess — Function
                                                              ess(
     samples::AbstractArray{<:Union{Missing,Real},3};
     kind=:bulk,
     autocov_method=AutocovMethod(),
@@ -55,3 +510,4 @@
 )
                                                              Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                              kwargs are forwarded to mcse.
                                                              source
                                                              MCMCDiagnosticTools.rafterydiag — Function
                                                              rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                              Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                              Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                              source
                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                              • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                              • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                              • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                              • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                              • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                              • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                              • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                              • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                              • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                              • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                              • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                              
+
diff --git a/v0.3.1/search/index.html b/v0.3.1/search/index.html
index 34a2c0cd..e36367f3 100644
--- a/v0.3.1/search/index.html
+++ b/v0.3.1/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
                                                              Loading search...
                                                                
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diff --git a/v0.3.10/index.html b/v0.3.10/index.html
index d588f268..f4d19aea 100644
--- a/v0.3.10/index.html
+++ b/v0.3.10/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                  GitHub
                                                                  MCMCDiagnosticTools
                                                                  MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                  Background
                                                                  Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                  Effective sample size and $\widehat{R}$
                                                                  MCMCDiagnosticTools.ess — Function
                                                                  ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                  GitHub
                                                                  MCMCDiagnosticTools
                                                                  MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                  Background
                                                                  Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                  Effective sample size and $\widehat{R}$
                                                                  MCMCDiagnosticTools.ess — Function
                                                                  ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                  Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                  kwargs are forwarded to mcse.
                                                                  source
                                                                  MCMCDiagnosticTools.rafterydiag — Function
                                                                  rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                  Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                  Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                  source
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                  
+
diff --git a/v0.3.2/index.html b/v0.3.2/index.html
index ae3bd813..b160141c 100644
--- a/v0.3.2/index.html
+++ b/v0.3.2/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                  Edit on GitHub
                                                                  MCMCDiagnosticTools
                                                                  Effective sample size and $\widehat{R}$
                                                                  MCMCDiagnosticTools.ess — Function
                                                                  ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                  Edit on GitHub
                                                                  MCMCDiagnosticTools
                                                                  Effective sample size and $\widehat{R}$
                                                                  MCMCDiagnosticTools.ess — Function
                                                                  ess(
     samples::AbstractArray{<:Union{Missing,Real},3};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                  Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                  kwargs are forwarded to mcse.
                                                                  source
                                                                  MCMCDiagnosticTools.rafterydiag — Function
                                                                  rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                  Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                  Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                  source
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                  
+
diff --git a/v0.3.2/search/index.html b/v0.3.2/search/index.html
index 05d5b429..b78ab5eb 100644
--- a/v0.3.2/search/index.html
+++ b/v0.3.2/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.3/index.html b/v0.3.3/index.html
index 683ce889..b1da9f7d 100644
--- a/v0.3.3/index.html
+++ b/v0.3.3/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                      Edit on GitHub
                                                                      MCMCDiagnosticTools
                                                                      Effective sample size and $\widehat{R}$
                                                                      MCMCDiagnosticTools.ess — Function
                                                                      ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                      Edit on GitHub
                                                                      MCMCDiagnosticTools
                                                                      Effective sample size and $\widehat{R}$
                                                                      MCMCDiagnosticTools.ess — Function
                                                                      ess(
     samples::AbstractArray{<:Union{Missing,Real},3};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                      kwargs are forwarded to mcse.
                                                                      source
                                                                      MCMCDiagnosticTools.rafterydiag — Function
                                                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                      source
                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                      • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                      • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                      
+
diff --git a/v0.3.3/search/index.html b/v0.3.3/search/index.html
index 42fe94be..d65f443b 100644
--- a/v0.3.3/search/index.html
+++ b/v0.3.3/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
                                                                      Loading search...
                                                                        
+Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.4/index.html b/v0.3.4/index.html
index b4d3410b..553a048d 100644
--- a/v0.3.4/index.html
+++ b/v0.3.4/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                          Edit on GitHub
                                                                          MCMCDiagnosticTools
                                                                          Effective sample size and $\widehat{R}$
                                                                          MCMCDiagnosticTools.ess — Function
                                                                          ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                          Edit on GitHub
                                                                          MCMCDiagnosticTools
                                                                          Effective sample size and $\widehat{R}$
                                                                          MCMCDiagnosticTools.ess — Function
                                                                          ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                          Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                          kwargs are forwarded to mcse.
                                                                          source
                                                                          MCMCDiagnosticTools.rafterydiag — Function
                                                                          rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                          Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                          Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                          source
                                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                          • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                          • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                          • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                          • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                          • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                          • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                          • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                          • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                          • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                          • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                          • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                          • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                          
+
diff --git a/v0.3.4/search/index.html b/v0.3.4/search/index.html
index 41c41359..a155ec45 100644
--- a/v0.3.4/search/index.html
+++ b/v0.3.4/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.5/index.html b/v0.3.5/index.html
index 41a8050f..004264df 100644
--- a/v0.3.5/index.html
+++ b/v0.3.5/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                              Edit on GitHub
                                                                              MCMCDiagnosticTools
                                                                              Effective sample size and $\widehat{R}$
                                                                              MCMCDiagnosticTools.ess — Function
                                                                              ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                              Edit on GitHub
                                                                              MCMCDiagnosticTools
                                                                              Effective sample size and $\widehat{R}$
                                                                              MCMCDiagnosticTools.ess — Function
                                                                              ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                              Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                              kwargs are forwarded to mcse.
                                                                              source
                                                                              MCMCDiagnosticTools.rafterydiag — Function
                                                                              rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                              Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                              Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                              source
                                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                              • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                              • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                              • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                              • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                              • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                              • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                              • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                              • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                              • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                              • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                              • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                              • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                              
+
diff --git a/v0.3.5/search/index.html b/v0.3.5/search/index.html
index 6c91953b..085898e9 100644
--- a/v0.3.5/search/index.html
+++ b/v0.3.5/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
                                                                              Loading search...
                                                                                
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diff --git a/v0.3.6/index.html b/v0.3.6/index.html
index 9df72d3f..82594e58 100644
--- a/v0.3.6/index.html
+++ b/v0.3.6/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                                  Edit on GitHub
                                                                                  MCMCDiagnosticTools
                                                                                  Effective sample size and $\widehat{R}$
                                                                                  MCMCDiagnosticTools.ess — Function
                                                                                  ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                                  Edit on GitHub
                                                                                  MCMCDiagnosticTools
                                                                                  Effective sample size and $\widehat{R}$
                                                                                  MCMCDiagnosticTools.ess — Function
                                                                                  ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                                  Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                                  kwargs are forwarded to mcse.
                                                                                  source
                                                                                  MCMCDiagnosticTools.rafterydiag — Function
                                                                                  rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                                  Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                                  Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                                  source
                                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                  • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                                  • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                  • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                                  • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                                  • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                                  • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                                  • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                                  • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                                  • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                                  • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                                  • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                                  • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                                  
+
diff --git a/v0.3.6/search/index.html b/v0.3.6/search/index.html
index 074c9616..c22c7d87 100644
--- a/v0.3.6/search/index.html
+++ b/v0.3.6/search/index.html
@@ -1,2 +1,458 @@
 
-Search · MCMCDiagnosticTools.jl
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+Search · MCMCDiagnosticTools.jl
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diff --git a/v0.3.7/index.html b/v0.3.7/index.html
index d161879b..2246cf4a 100644
--- a/v0.3.7/index.html
+++ b/v0.3.7/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                                      kwargs are forwarded to mcse.
                                                                                      source
                                                                                      MCMCDiagnosticTools.rafterydiag — Function
                                                                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                                      source
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                                      • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                                      • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                                      
+
diff --git a/v0.3.8/index.html b/v0.3.8/index.html
index ef44ce20..62139840 100644
--- a/v0.3.8/index.html
+++ b/v0.3.8/index.html
@@ -1,5 +1,460 @@
 
-Home · MCMCDiagnosticTools.jl
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                                      kwargs are forwarded to mcse.
                                                                                      source
                                                                                      MCMCDiagnosticTools.rafterydiag — Function
                                                                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                                      source
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                                      • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                                      • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                                      
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-Home · MCMCDiagnosticTools.jl
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
+Home · MCMCDiagnosticTools.jl
+
+
+
+
+
+
                                                                                      GitHub
                                                                                      MCMCDiagnosticTools
                                                                                      MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.
                                                                                      Background
                                                                                      Some methods were originally part of Mamba.jl and then MCMCChains.jl. This package is a joint collaboration between the Turing and ArviZ projects.
                                                                                      Effective sample size and $\widehat{R}$
                                                                                      MCMCDiagnosticTools.ess — Function
                                                                                      ess(
     samples::AbstractArray{<:Union{Missing,Real}};
     kind=:bulk,
     relative::Bool=false,
@@ -56,3 +511,4 @@
 )
                                                                                      Compute the Heidelberger and Welch diagnostic [Heidelberger1983]. This diagnostic tests for non-convergence (non-stationarity) and whether ratios of estimation interval halfwidths to means are within a target ratio. Stationarity is rejected (0) for significant test p-values. Halfwidth tests are rejected (0) if observed ratios are greater than the target, as is the case for s2 and beta[1].
                                                                                      kwargs are forwarded to mcse.
                                                                                      source
                                                                                      MCMCDiagnosticTools.rafterydiag — Function
                                                                                      rafterydiag(
     x::AbstractVector{<:Real}; q=0.025, r=0.005, s=0.95, eps=0.001, range=1:length(x)
 )
                                                                                      Compute the Raftery and Lewis diagnostic [Raftery1992]. This diagnostic is used to determine the number of iterations required to estimate a specified quantile q within a desired degree of accuracy.  The diagnostic is designed to determine the number of autocorrelated samples required to estimate a specified quantile $\theta_q$, such that $\Pr(\theta \le \theta_q) = q$, within a desired degree of accuracy. In particular, if $\hat{\theta}_q$ is the estimand and $\Pr(\theta \le \hat{\theta}_q) = \hat{P}_q$ the estimated cumulative probability, then accuracy is specified in terms of r and s, where $\Pr(q - r < \hat{P}_q < q + r) = s$. Thinning may be employed in the calculation of the diagnostic to satisfy its underlying assumptions. However, users may not want to apply the same (or any) thinning when estimating posterior summary statistics because doing so results in a loss of information. Accordingly, sample sizes estimated by the diagnostic tend to be conservative (too large).
                                                                                      Furthermore, the argument r specifies the margin of error for estimated cumulative probabilities and s the probability for the margin of error. eps specifies the tolerance within which the probabilities of transitioning from initial to retained iterations are within the equilibrium probabilities for the chain. This argument determines the number of samples to discard as a burn-in sequence and is typically left at its default value.
                                                                                      source
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • Geyer1992Geyer, C. J. (1992). Practical Markov Chain Monte Carlo. Statistical Science, 473-483.
                                                                                      • VehtariGelman2021Vehtari, A., Gelman, A., Simpson, D., Carpenter, B., & Bürkner, P. C. (2021). Rank-normalization, folding, and localization: An improved $\widehat {R}$ for assessing convergence of MCMC. Bayesian Analysis. doi: 10.1214/20-BA1221 arXiv: 1903.08008
                                                                                      • BDA3Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., & Rubin, D. B. (2013). Bayesian data analysis. CRC press.
                                                                                      • FlegalJones2011Flegal JM, Jones GL. (2011) Implementing MCMC: estimating with confidence.                 Handbook of Markov Chain Monte Carlo. pp. 175-97.                 pdf
                                                                                      • Flegal2012Flegal JM. (2012) Applicability of subsampling bootstrap methods in Markov chain Monte Carlo.            Monte Carlo and Quasi-Monte Carlo Methods 2010. pp. 363-72.            doi: 10.1007/978-3-642-27440-4_18
                                                                                      • Betancourt2018Betancourt M. (2018). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv:1701.02434v2 [stat.ME]
                                                                                      • Betancourt2016Betancourt M. (2016). Diagnosing Suboptimal Cotangent Disintegrations in Hamiltonian Monte Carlo. arXiv:1604.00695v1 [stat.ME]
                                                                                      • Gelman1992Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical science, 7(4), 457-472.
                                                                                      • Brooks1998Brooks, S. P., & Gelman, A. (1998). General methods for monitoring convergence of iterative simulations. Journal of computational and graphical statistics, 7(4), 434-455.
                                                                                      • Geweke1991Geweke, J. F. (1991). Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments (No. 148). Federal Reserve Bank of Minneapolis.
                                                                                      • Heidelberger1983Heidelberger, P., & Welch, P. D. (1983). Simulation run length control in the presence of an initial transient. Operations Research, 31(6), 1109-1144.
                                                                                      • Raftery1992A L Raftery and S Lewis. Bayesian Statistics, chapter How Many Iterations in the Gibbs Sampler? Volume 4. Oxford University Press, New York, 1992.
                                                                                      
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