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<!DOCTYPE html>
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<title>pypmc — pypmc 1.2.2 documentation</title>
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pypmc
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1.2.2
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<section id="pypmc">
<h1>pypmc<a class="headerlink" href="#pypmc" title="Permalink to this heading"></a></h1>
<p><code class="docutils literal notranslate"><span class="pre">pypmc</span></code> is a python package focusing on adaptive importance
sampling. It can be used for integration and sampling from a
user-defined target density. A typical application is Bayesian
inference, where one wants to sample from the posterior to marginalize
over parameters and to compute the evidence. The key idea is to create
a good proposal density by adapting a mixture of Gaussian or student’s
t components to the target density. The package is able to efficiently
integrate multimodal functions in up to about 30-40 dimensions at the
level of 1% accuracy or less. For many problems, this is achieved
without requiring any manual input from the user about details of the
function. Importance sampling supports parallelization on multiple
machines via <code class="docutils literal notranslate"><span class="pre">mpi4py</span></code>.</p>
<p>Useful tools that can be used stand-alone include:</p>
<ul class="simple">
<li><p>importance sampling (sampling & integration)</p></li>
<li><p>adaptive Markov chain Monte Carlo (sampling)</p></li>
<li><p>variational Bayes (clustering)</p></li>
<li><p>population Monte Carlo (clustering)</p></li>
</ul>
</section>
<section id="how-to-use-this-documentation">
<h1>How to use this documentation<a class="headerlink" href="#how-to-use-this-documentation" title="Permalink to this heading"></a></h1>
<p>If you don’t know yet whether <code class="docutils literal notranslate"><span class="pre">pypmc</span></code> is the right tool for your
needs, you should first read through the overview. There, we introduce
the basic algorithms implemented by <code class="docutils literal notranslate"><span class="pre">pypmc</span></code>. If you want to give
<code class="docutils literal notranslate"><span class="pre">pypmc</span></code> a try, just follow the installation instructions. The user
guide then explains adaptive importance sampling. In the examples
section, we show how to use the algorithms on simple problems. Take
them as a starting point to work on your problem. Finally, look
through the reference guide if you need help on a specific function or
class.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="introduction.html">1. Overview</a><ul>
<li class="toctree-l2"><a class="reference internal" href="introduction.html#initial-proposal-density">1.1. Initial proposal density</a></li>
<li class="toctree-l2"><a class="reference internal" href="introduction.html#proposal-updates">1.2. Proposal updates</a></li>
<li class="toctree-l2"><a class="reference internal" href="introduction.html#pmc">1.3. PMC</a></li>
<li class="toctree-l2"><a class="reference internal" href="introduction.html#variational-bayes">1.4. Variational Bayes</a></li>
<li class="toctree-l2"><a class="reference internal" href="introduction.html#performance">1.5. Performance</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="installation.html">2. Installation</a><ul>
<li class="toctree-l2"><a class="reference internal" href="installation.html#developer-notes">2.1. Developer notes</a><ul>
<li class="toctree-l3"><a class="reference internal" href="installation.html#debian-or-derivative">2.1.1. Debian or derivative</a></li>
<li class="toctree-l3"><a class="reference internal" href="installation.html#conda">2.1.2. Conda</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="user_guide.html">3. User guide</a><ul>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#densities">3.1. Densities</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#component-density">3.1.1. Component density</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#mixture-density">3.1.2. Mixture density</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#indicator-function">3.2. Indicator function</a></li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#markov-chain">3.3. Markov chain</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#initialization">3.3.1. Initialization</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#adaptation">3.3.2. Adaptation</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#importance-sampling">3.4. Importance sampling</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#standard">3.4.1. Standard</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#deterministic-mixture">3.4.2. Deterministic mixture</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#comparison">3.4.3. Comparison</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#pmc">3.5. PMC</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#basic-approach">3.5.1. Basic approach</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#id6">3.5.2. Student’s t</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#pmc-with-multiple-em-steps">3.5.3. PMC with multiple EM steps</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#variational-bayes">3.6. Variational Bayes</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#classic-version">3.6.1. Classic version</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#mixture-reduction">3.7. Mixture reduction</a><ul>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#hierarchical-clustering">3.7.1. Hierarchical clustering</a></li>
<li class="toctree-l3"><a class="reference internal" href="user_guide.html#vbmerge">3.7.2. VBmerge</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="user_guide.html#putting-it-all-together">3.8. Putting it all together</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="examples.html">4. Examples</a><ul>
<li class="toctree-l2"><a class="reference internal" href="examples.html#mcmc">4.1. MCMC</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#pmc">4.2. PMC</a><ul>
<li class="toctree-l3"><a class="reference internal" href="examples.html#serial">4.2.1. Serial</a></li>
<li class="toctree-l3"><a class="reference internal" href="examples.html#parallel">4.2.2. Parallel</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#grouping-by-gelman-rubin-r-value">4.3. Grouping by Gelman-Rubin R value</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#variational-bayes">4.4. Variational Bayes</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#mixture-reduction">4.5. Mixture reduction</a></li>
<li class="toctree-l2"><a class="reference internal" href="examples.html#mcmc-variational-bayes">4.6. MCMC + variational Bayes</a></li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="references.html">5. References</a></li>
<li class="toctree-l1"><a class="reference internal" href="api.html">6. Reference Guide</a><ul>
<li class="toctree-l2"><a class="reference internal" href="api.html#module-pypmc.density">6.1. Probability density</a><ul>
<li class="toctree-l3"><a class="reference internal" href="api.html#pypmc.density.base.LocalDensity"><code class="docutils literal notranslate"><span class="pre">LocalDensity</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#pypmc.density.base.ProbabilityDensity"><code class="docutils literal notranslate"><span class="pre">ProbabilityDensity</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.density.gauss">6.1.1. Gauss</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.density.student_t">6.1.2. StudentT</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.density.mixture">6.1.3. Mixture</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="api.html#module-pypmc.sampler">6.2. Sampler</a><ul>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.sampler.markov_chain">6.2.1. Markov Chain</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.sampler.importance_sampling">6.2.2. Importance Sampling</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="api.html#module-pypmc.mix_adapt">6.3. Mixture adaptation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.mix_adapt.hierarchical">6.3.1. Hierarchical clustering</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.mix_adapt.variational">6.3.2. Variational Bayes</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.mix_adapt.pmc">6.3.3. PMC</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.mix_adapt.r_value">6.3.4. Gelman-Rubin R-value</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="api.html#module-pypmc.tools">6.4. Tools</a><ul>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.tools.convergence">6.4.1. Convergence diagnostics</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#history">6.4.2. History</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.tools.indicator">6.4.3. Indicator</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#module-pypmc.tools.parallel_sampler">6.4.4. Parallel sampler</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#partition">6.4.5. Partition</a></li>
<li class="toctree-l3"><a class="reference internal" href="api.html#plot">6.4.6. Plot</a></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</section>
<section id="indices-and-tables">
<h1>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this heading"></a></h1>
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