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 <div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>MCMCDiagnosticTools.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Background"><span>Background</span></a></li><li><a class="tocitem" href="#Effective-sample-size-and-\\widehat{R}"><span>Effective sample size and <span>$\widehat{R}$</span></span></a></li><li><a class="tocitem" href="#Monte-Carlo-standard-error"><span>Monte Carlo standard error</span></a></li><li><a class="tocitem" href="#R-diagnostic"><span>R⋆ diagnostic</span></a></li><li><a class="tocitem" href="#Bayesian-fraction-of-missing-information"><span>Bayesian fraction of missing information</span></a></li><li><a class="tocitem" href="#Other-diagnostics"><span>Other diagnostics</span></a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/TuringLang/MCMCDiagnosticTools.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/TuringLang/MCMCDiagnosticTools.jl/blob/main/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="MCMCDiagnosticTools"><a class="docs-heading-anchor" href="#MCMCDiagnosticTools">MCMCDiagnosticTools</a><a id="MCMCDiagnosticTools-1"></a><a class="docs-heading-anchor-permalink" href="#MCMCDiagnosticTools" title="Permalink"></a></h1><p>MCMCDiagnosticTools provides functionality for diagnosing samples generated using Markov Chain Monte Carlo.</p><h2 id="Background"><a class="docs-heading-anchor" href="#Background">Background</a><a id="Background-1"></a><a class="docs-heading-anchor-permalink" href="#Background" title="Permalink"></a></h2><p>Some methods were originally part of <a href="https://github.com/brian-j-smith/Mamba.jl">Mamba.jl</a> and then <a href="https://github.com/TuringLang/MCMCChains.jl">MCMCChains.jl</a>. This package is a joint collaboration between the <a href="https://turinglang.org/">Turing</a> and <a href="https://www.arviz.org/">ArviZ</a> projects.</p><h2 id="Effective-sample-size-and-\\widehat{R}"><a class="docs-heading-anchor" href="#Effective-sample-size-and-\\widehat{R}">Effective sample size and <span>$\widehat{R}$</span></a><a id="Effective-sample-size-and-\\widehat{R}-1"></a><a class="docs-heading-anchor-permalink" href="#Effective-sample-size-and-\\widehat{R}" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="MCMCDiagnosticTools.ess" href="#MCMCDiagnosticTools.ess"><code>MCMCDiagnosticTools.ess</code></a> — <span class="docstring-category">Function</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">ess(
     samples::AbstractArray{&lt;:Union{Missing,Real}};
     kind=:bulk,

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