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<!DOCTYPE html>
<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>AdvancedMH.jl · AdvancedMH</title><meta name="title" content="AdvancedMH.jl · AdvancedMH"/><meta property="og:title" content="AdvancedMH.jl · AdvancedMH"/><meta property="twitter:title" content="AdvancedMH.jl · AdvancedMH"/><meta name="description" content="Documentation for AdvancedMH."/><meta property="og:description" content="Documentation for AdvancedMH."/><meta property="twitter:description" content="Documentation for AdvancedMH."/><script data-outdated-warner src="../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" 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href="../">AdvancedMH.jl</a></li><li class="is-active"><a class="tocitem" href>AdvancedMH.jl</a><ul class="internal"><li><a class="tocitem" href="#Structs"><span>Structs</span></a></li><li><a class="tocitem" href="#Functions"><span>Functions</span></a></li><li><a class="tocitem" href="#Samplers"><span>Samplers</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>AdvancedMH.jl</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>AdvancedMH.jl</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/TuringLang/AdvancedMH.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/AdvancedMH.jl/blob/master/docs/src/api.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="AdvancedMH.jl"><a class="docs-heading-anchor" href="#AdvancedMH.jl">AdvancedMH.jl</a><a id="AdvancedMH.jl-1"></a><a class="docs-heading-anchor-permalink" href="#AdvancedMH.jl" title="Permalink"></a></h1><p>Documentation for AdvancedMH.jl</p><h2 id="Structs"><a class="docs-heading-anchor" href="#Structs">Structs</a><a id="Structs-1"></a><a class="docs-heading-anchor-permalink" href="#Structs" 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="AdvancedMH.MetropolisHastings" href="#AdvancedMH.MetropolisHastings"><code>AdvancedMH.MetropolisHastings</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">MetropolisHastings{D}</code></pre><p><code>MetropolisHastings</code> has one field, <code>proposal</code>. <code>proposal</code> is a <code>Proposal</code>, <code>NamedTuple</code> of <code>Proposal</code>, or <code>Array{Proposal}</code> in the shape of your data. For example, if you wanted the sampler to return a <code>NamedTuple</code> with shape</p><pre><code class="language-julia hljs">x = (a = 1.0, b=3.8)</code></pre><p>The proposal would be</p><pre><code class="language-julia hljs">proposal = (a=StaticProposal(Normal(0,1)), b=StaticProposal(Normal(0,1)))</code></pre><p>Other allowed proposals are</p><pre><code class="nohighlight hljs">p1 = StaticProposal(Normal(0,1))
p2 = StaticProposal([Normal(0,1), InverseGamma(2,3)])
p3 = StaticProposal((a=Normal(0,1), b=InverseGamma(2,3)))
p4 = StaticProposal((x=1.0) -&gt; Normal(x, 1))</code></pre><p>The sampler is constructed using</p><pre><code class="language-julia hljs">spl = MetropolisHastings(proposal)</code></pre><p>When using <code>MetropolisHastings</code> with the function <code>sample</code>, the following keyword arguments are allowed:</p><ul><li><code>initial_params</code> defines the initial parameterization for your model. If</li></ul><p>none is given, the initial parameters will be drawn from the sampler&#39;s proposals.</p><ul><li><code>param_names</code> is a vector of strings to be assigned to parameters. This is only</li></ul><p>used if <code>chain_type=Chains</code>.</p><ul><li><code>chain_type</code> is the type of chain you would like returned to you. Supported</li></ul><p>types are <code>chain_type=Chains</code> if <code>MCMCChains</code> is imported, or <code>chain_type=StructArray</code> if <code>StructArrays</code> is imported.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/TuringLang/AdvancedMH.jl/blob/ef34dcda818c2c095fcb60e8fb1c266d191e7a66/src/mh-core.jl#L1-L43">source</a></section></article><h2 id="Functions"><a class="docs-heading-anchor" href="#Functions">Functions</a><a id="Functions-1"></a><a class="docs-heading-anchor-permalink" href="#Functions" 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="AdvancedMH.DensityModel" href="#AdvancedMH.DensityModel"><code>AdvancedMH.DensityModel</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">DensityModel{F} &lt;: AbstractModel</code></pre><p><code>DensityModel</code> wraps around a self-contained log-liklihood function <code>logdensity</code>.</p><p>Example:</p><pre><code class="language-julia hljs">l(x) = logpdf(Normal(), x)
DensityModel(l)</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/TuringLang/AdvancedMH.jl/blob/ef34dcda818c2c095fcb60e8fb1c266d191e7a66/src/AdvancedMH.jl#L40-L51">source</a></section></article><h2 id="Samplers"><a class="docs-heading-anchor" href="#Samplers">Samplers</a><a id="Samplers-1"></a><a class="docs-heading-anchor-permalink" href="#Samplers" 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="AdvancedMH.RobustAdaptiveMetropolis" href="#AdvancedMH.RobustAdaptiveMetropolis"><code>AdvancedMH.RobustAdaptiveMetropolis</code></a> — <span class="docstring-category">Type</span><span class="is-flex-grow-1 docstring-article-toggle-button" title="Collapse docstring"></span></header><section><div><pre><code class="language-julia hljs">RobustAdaptiveMetropolis</code></pre><p>Robust Adaptive Metropolis-Hastings (RAM).</p><p>This is a simple implementation of the RAM algorithm described in <sup class="footnote-reference"><a id="citeref-VIH12" href="#footnote-VIH12">[VIH12]</a></sup>.</p><p><strong>Fields</strong></p><ul><li><p><code>α</code>: target acceptance rate. Default: 0.234.</p></li><li><p><code>γ</code>: negative exponent of the adaptation decay rate. Default: <code>0.6</code>.</p></li><li><p><code>S</code>: initial lower-triangular Cholesky factor of the covariance matrix. If specified, should be convertible into a <code>LowerTriangular</code>. Default: <code>nothing</code>, which is interpreted as the identity matrix.</p></li><li><p><code>eigenvalue_lower_bound</code>: lower bound on eigenvalues of the adapted Cholesky factor. Default: <code>0.0</code>.</p></li><li><p><code>eigenvalue_upper_bound</code>: upper bound on eigenvalues of the adapted Cholesky factor. Default: <code>Inf</code>.</p></li></ul><p><strong>Examples</strong></p><p>The following demonstrates how to implement a simple Gaussian model and sample from it using the RAM algorithm.</p><pre><code class="language-julia-repl hljs">julia&gt; using AdvancedMH, Distributions, MCMCChains, LogDensityProblems, LinearAlgebra

julia&gt; # Define a Gaussian with zero mean and some covariance.
struct Gaussian{A}
Σ::A
end

julia&gt; # Implement the LogDensityProblems interface.
LogDensityProblems.dimension(model::Gaussian) = size(model.Σ, 1)

julia&gt; function LogDensityProblems.logdensity(model::Gaussian, x)
d = LogDensityProblems.dimension(model)
return logpdf(MvNormal(zeros(d),model.Σ), x)
end

julia&gt; LogDensityProblems.capabilities(::Gaussian) = LogDensityProblems.LogDensityOrder{0}()

julia&gt; # Construct the model. We&#39;ll use a correlation of 0.5.
model = Gaussian([1.0 0.5; 0.5 1.0]);

julia&gt; # Number of samples we want in the resulting chain.
num_samples = 10_000;

julia&gt; # Number of warmup steps, i.e. the number of steps to adapt the covariance of the proposal.
# Note that these are not included in the resulting chain, as `discard_initial=num_warmup`
# by default in the `sample` call. To include them, pass `discard_initial=0` to `sample`.
num_warmup = 10_000;

julia&gt; # Sample!
chain = sample(
model,
RobustAdaptiveMetropolis(),
num_samples;
chain_type=Chains, num_warmup, progress=false, initial_params=zeros(2)
);

julia&gt; isapprox(cov(Array(chain)), model.Σ; rtol = 0.2)
true</code></pre><p>It&#39;s also possible to restrict the eigenvalues to avoid either too small or too large values. See p. 13 in <sup class="footnote-reference"><a id="citeref-VIH12" href="#footnote-VIH12">[VIH12]</a></sup>.</p><pre><code class="language-julia-repl hljs">julia&gt; chain = sample(
model,
RobustAdaptiveMetropolis(eigenvalue_lower_bound=0.1, eigenvalue_upper_bound=2.0),
num_samples;
chain_type=Chains, num_warmup, progress=false, initial_params=zeros(2)
);

julia&gt; norm(cov(Array(chain)) - [1.0 0.5; 0.5 1.0]) &lt; 0.2
true</code></pre><p><strong>References</strong></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/TuringLang/AdvancedMH.jl/blob/ef34dcda818c2c095fcb60e8fb1c266d191e7a66/src/RobustAdaptiveMetropolis.jl#L2-L74">source</a></section></article><section class="footnotes is-size-7"><ul><li class="footnote" id="footnote-VIH12"><a class="tag is-link" href="#citeref-VIH12">VIH12</a>Vihola (2012) Robust adaptive Metropolis algorithm with coerced acceptance rate, Statistics and computing.</li></ul></section></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« AdvancedMH.jl</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="auto">Automatic (OS)</option><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option><option value="catppuccin-latte">catppuccin-latte</option><option value="catppuccin-frappe">catppuccin-frappe</option><option value="catppuccin-macchiato">catppuccin-macchiato</option><option value="catppuccin-mocha">catppuccin-mocha</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> version 1.8.0 on <span class="colophon-date" title="Wednesday 11 December 2024 09:16">Wednesday 11 December 2024</span>. Using Julia version 1.11.2.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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