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<!DOCTYPE html>
<html class="writer-html5" lang="en" >
<head>
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<title>6. Reference Guide — pypmc 1.2.2 documentation</title>
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pypmc
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<div class="version">
1.2.2
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<ul class="current">
<li class="toctree-l1"><a class="reference internal" href="introduction.html">1. Overview</a></li>
<li class="toctree-l1"><a class="reference internal" href="installation.html">2. Installation</a></li>
<li class="toctree-l1"><a class="reference internal" href="user_guide.html">3. User guide</a></li>
<li class="toctree-l1"><a class="reference internal" href="examples.html">4. Examples</a></li>
<li class="toctree-l1"><a class="reference internal" href="references.html">5. References</a></li>
<li class="toctree-l1 current"><a class="current reference internal" href="#">6. Reference Guide</a><ul>
<li class="toctree-l2"><a class="reference internal" href="#module-pypmc.density">6.1. Probability density</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#pypmc.density.base.LocalDensity"><code class="docutils literal notranslate"><span class="pre">LocalDensity</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.base.LocalDensity.evaluate"><code class="docutils literal notranslate"><span class="pre">LocalDensity.evaluate</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.base.LocalDensity.propose"><code class="docutils literal notranslate"><span class="pre">LocalDensity.propose</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#pypmc.density.base.ProbabilityDensity"><code class="docutils literal notranslate"><span class="pre">ProbabilityDensity</span></code></a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.base.ProbabilityDensity.evaluate"><code class="docutils literal notranslate"><span class="pre">ProbabilityDensity.evaluate</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.base.ProbabilityDensity.multi_evaluate"><code class="docutils literal notranslate"><span class="pre">ProbabilityDensity.multi_evaluate</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.base.ProbabilityDensity.propose"><code class="docutils literal notranslate"><span class="pre">ProbabilityDensity.propose</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.density.gauss">6.1.1. Gauss</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.gauss.Gauss"><code class="docutils literal notranslate"><span class="pre">Gauss</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.gauss.LocalGauss"><code class="docutils literal notranslate"><span class="pre">LocalGauss</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.density.student_t">6.1.2. StudentT</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.student_t.LocalStudentT"><code class="docutils literal notranslate"><span class="pre">LocalStudentT</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.student_t.StudentT"><code class="docutils literal notranslate"><span class="pre">StudentT</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.density.mixture">6.1.3. Mixture</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.mixture.MixtureDensity"><code class="docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.mixture.create_gaussian_mixture"><code class="docutils literal notranslate"><span class="pre">create_gaussian_mixture</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.mixture.create_t_mixture"><code class="docutils literal notranslate"><span class="pre">create_t_mixture</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.mixture.recover_gaussian_mixture"><code class="docutils literal notranslate"><span class="pre">recover_gaussian_mixture</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.density.mixture.recover_t_mixture"><code class="docutils literal notranslate"><span class="pre">recover_t_mixture</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="#module-pypmc.sampler">6.2. Sampler</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.sampler.markov_chain">6.2.1. Markov Chain</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.markov_chain.MarkovChain"><code class="docutils literal notranslate"><span class="pre">MarkovChain</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.markov_chain.AdaptiveMarkovChain"><code class="docutils literal notranslate"><span class="pre">AdaptiveMarkovChain</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.sampler.importance_sampling">6.2.2. Importance Sampling</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.importance_sampling.calculate_covariance"><code class="docutils literal notranslate"><span class="pre">calculate_covariance</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.importance_sampling.calculate_expectation"><code class="docutils literal notranslate"><span class="pre">calculate_expectation</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.importance_sampling.calculate_mean"><code class="docutils literal notranslate"><span class="pre">calculate_mean</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.importance_sampling.combine_weights"><code class="docutils literal notranslate"><span class="pre">combine_weights</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.sampler.importance_sampling.ImportanceSampler"><code class="docutils literal notranslate"><span class="pre">ImportanceSampler</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="#module-pypmc.mix_adapt">6.3. Mixture adaptation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.mix_adapt.hierarchical">6.3.1. Hierarchical clustering</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.hierarchical.Hierarchical"><code class="docutils literal notranslate"><span class="pre">Hierarchical</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.hierarchical.kullback_leibler"><code class="docutils literal notranslate"><span class="pre">kullback_leibler</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.mix_adapt.variational">6.3.2. Variational Bayes</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.Dirichlet_log_C"><code class="docutils literal notranslate"><span class="pre">Dirichlet_log_C</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.GaussianInference"><code class="docutils literal notranslate"><span class="pre">GaussianInference</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.VBMerge"><code class="docutils literal notranslate"><span class="pre">VBMerge</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.Wishart_H"><code class="docutils literal notranslate"><span class="pre">Wishart_H</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.Wishart_expect_log_lambda"><code class="docutils literal notranslate"><span class="pre">Wishart_expect_log_lambda</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.variational.Wishart_log_B"><code class="docutils literal notranslate"><span class="pre">Wishart_log_B</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.mix_adapt.pmc">6.3.3. PMC</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.pmc.PMC"><code class="docutils literal notranslate"><span class="pre">PMC</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.pmc.gaussian_pmc"><code class="docutils literal notranslate"><span class="pre">gaussian_pmc</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.pmc.student_t_pmc"><code class="docutils literal notranslate"><span class="pre">student_t_pmc</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.mix_adapt.r_value">6.3.4. Gelman-Rubin R-value</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.r_value.make_r_gaussmix"><code class="docutils literal notranslate"><span class="pre">make_r_gaussmix</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.r_value.make_r_tmix"><code class="docutils literal notranslate"><span class="pre">make_r_tmix</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.r_value.r_group"><code class="docutils literal notranslate"><span class="pre">r_group</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.mix_adapt.r_value.r_value"><code class="docutils literal notranslate"><span class="pre">r_value</span></code></a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="#module-pypmc.tools">6.4. Tools</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.tools.convergence">6.4.1. Convergence diagnostics</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.convergence.ess"><code class="docutils literal notranslate"><span class="pre">ess</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.convergence.perp"><code class="docutils literal notranslate"><span class="pre">perp</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#history">6.4.2. History</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.History"><code class="docutils literal notranslate"><span class="pre">History</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.tools.indicator">6.4.3. Indicator</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.indicator.ball"><code class="docutils literal notranslate"><span class="pre">ball</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.indicator.hyperrectangle"><code class="docutils literal notranslate"><span class="pre">hyperrectangle</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.indicator.merge_function_with_indicator"><code class="docutils literal notranslate"><span class="pre">merge_function_with_indicator</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#module-pypmc.tools.parallel_sampler">6.4.4. Parallel sampler</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.parallel_sampler.MPISampler"><code class="docutils literal notranslate"><span class="pre">MPISampler</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#partition">6.4.5. Partition</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.partition"><code class="docutils literal notranslate"><span class="pre">partition</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.patch_data"><code class="docutils literal notranslate"><span class="pre">patch_data</span></code></a></li>
</ul>
</li>
<li class="toctree-l3"><a class="reference internal" href="#plot">6.4.6. Plot</a><ul>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.plot_mixture"><code class="docutils literal notranslate"><span class="pre">plot_mixture</span></code></a></li>
<li class="toctree-l4"><a class="reference internal" href="#pypmc.tools.plot_responsibility"><code class="docutils literal notranslate"><span class="pre">plot_responsibility</span></code></a></li>
</ul>
</li>
</ul>
</li>
</ul>
</li>
</ul>
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<section id="reference-guide">
<h1><span class="section-number">6. </span>Reference Guide<a class="headerlink" href="#reference-guide" title="Permalink to this heading"></a></h1>
<section id="module-pypmc.density">
<span id="probability-density"></span><h2><span class="section-number">6.1. </span>Probability density<a class="headerlink" href="#module-pypmc.density" title="Permalink to this heading"></a></h2>
<p>Collect probability densities</p>
<span class="target" id="module-pypmc.density.base"></span><p>Collect abstract base probability density classes</p>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.base.LocalDensity">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.base.</span></span><span class="sig-name descname"><span class="pre">LocalDensity</span></span><a class="reference internal" href="_modules/pypmc/density/base.html#LocalDensity"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.LocalDensity" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>Abstract base class for a local probability density. Can be used as
proposal for the Markov chain sampler.</p>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.base.LocalDensity.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/density/base.html#LocalDensity.evaluate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.LocalDensity.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code> given <code class="docutils literal notranslate"><span class="pre">y</span></code>,
namely log(q(x|y)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Vector-like array; the proposed point</p></li>
<li><p><strong>y</strong> – Vector-like array; the current point</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.base.LocalDensity.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/density/base.html#LocalDensity.propose"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.LocalDensity.propose" title="Permalink to this definition"></a></dt>
<dd><p>Propose a new point given <code class="docutils literal notranslate"><span class="pre">y</span></code> using the random number
generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> – Vector-like array; the current position</p></li>
<li><p><strong>rng</strong> – State of a random number generator like numpy.random.mtrand</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.base.ProbabilityDensity">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.base.</span></span><span class="sig-name descname"><span class="pre">ProbabilityDensity</span></span><a class="reference internal" href="_modules/pypmc/density/base.html#ProbabilityDensity"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.ProbabilityDensity" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p>Abstract Base class of a probability density. Can be used as proposal
for the importance sampler.</p>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.base.ProbabilityDensity.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/density/base.html#ProbabilityDensity.evaluate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.ProbabilityDensity.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> – Vector-like array; the proposed point.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.base.ProbabilityDensity.multi_evaluate">
<span class="sig-name descname"><span class="pre">multi_evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">out</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/density/base.html#ProbabilityDensity.multi_evaluate"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.ProbabilityDensity.multi_evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x))
for each row in x.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Matrix-like array; the proposed points. Expect i-th accessible
as <code class="docutils literal notranslate"><span class="pre">x[i]</span></code>.</p></li>
<li><p><strong>out</strong> – Vector-like array, length==``len(x)``, optional; If provided,
the output is written into this array.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.base.ProbabilityDensity.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/density/base.html#ProbabilityDensity.propose"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.density.base.ProbabilityDensity.propose" title="Permalink to this definition"></a></dt>
<dd><p>Propose N points using the random number generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>N</strong> – Integer; the number of random points to be proposed</p></li>
<li><p><strong>rng</strong> – State of a random number generator like <code class="docutils literal notranslate"><span class="pre">numpy.random.mtrand</span></code></p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<section id="module-pypmc.density.gauss">
<span id="gauss"></span><h3><span class="section-number">6.1.1. </span>Gauss<a class="headerlink" href="#module-pypmc.density.gauss" title="Permalink to this heading"></a></h3>
<p>Collect Gaussian probability densities</p>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.gauss.Gauss">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.gauss.</span></span><span class="sig-name descname"><span class="pre">Gauss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.Gauss" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pypmc.density.base.ProbabilityDensity" title="pypmc.density.base.ProbabilityDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProbabilityDensity</span></code></a></p>
<p>A Gaussian probability density. Can be used as component for
MixtureDensities.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mu</strong> – Vector-like array; the gaussian’s mean <span class="math notranslate nohighlight">\(\mu\)</span></p></li>
<li><p><strong>sigma</strong> – Matrix-like array; the gaussian’s covariance matrix <span class="math notranslate nohighlight">\(\Sigma\)</span></p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.Gauss.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.Gauss.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> – Vector-like array; the proposed point.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.Gauss.multi_evaluate">
<span class="sig-name descname"><span class="pre">multi_evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">out=None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.Gauss.multi_evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x))
for each row in x.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Matrix-like array; the proposed points. Expect i-th accessible
as <code class="docutils literal notranslate"><span class="pre">x[i]</span></code>.</p></li>
<li><p><strong>out</strong> – Vector-like array, length==``len(x)``, optional; If provided,
the output is written into this array.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.Gauss.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">int</span> <span class="pre">N=1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng=_np.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.Gauss.propose" title="Permalink to this definition"></a></dt>
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span></dt>
<dd><p>Propose N points using the random number generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>N</strong> – Integer; the number of random points to be proposed</p></li>
<li><p><strong>rng</strong> – State of a random number generator like <code class="docutils literal notranslate"><span class="pre">numpy.random.mtrand</span></code></p></li>
</ul>
</dd>
</dl>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must meet the requirements of
<a class="reference internal" href="#pypmc.density.gauss.LocalGauss.propose" title="pypmc.density.gauss.LocalGauss.propose"><code class="xref py py-meth docutils literal notranslate"><span class="pre">LocalGauss.propose</span></code></a>.</p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.Gauss.update">
<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.Gauss.update" title="Permalink to this definition"></a></dt>
<dd><p>Re-initialize the density with new mean and covariance matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mu</strong> – Vector-like array; the gaussian’s mean <span class="math notranslate nohighlight">\(\mu\)</span></p></li>
<li><p><strong>sigma</strong> – Matrix-like array; the gaussian’s covariance matrix
<span class="math notranslate nohighlight">\(\Sigma\)</span></p></li>
</ul>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>On <code class="docutils literal notranslate"><span class="pre">LinAlgError</span></code>, the old <code class="docutils literal notranslate"><span class="pre">mu</span></code> and <code class="docutils literal notranslate"><span class="pre">sigma</span></code> are plugged
in and the proposal remains in a valid state.</p>
</div>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.gauss.LocalGauss">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.gauss.</span></span><span class="sig-name descname"><span class="pre">LocalGauss</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.LocalGauss" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pypmc.density.base.LocalDensity" title="pypmc.density.base.LocalDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">LocalDensity</span></code></a></p>
<p>A multivariate local Gaussian density with redefinable covariance.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sigma</strong> – Matrix-like array; covariance-matrix.</p>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.LocalGauss.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.LocalGauss.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code> given <code class="docutils literal notranslate"><span class="pre">y</span></code>,
namely log(q(x|y)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Vector-like array; the proposed point</p></li>
<li><p><strong>y</strong> – Vector-like array; the current point</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.LocalGauss.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">_np.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.LocalGauss.propose" title="Permalink to this definition"></a></dt>
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span></dt>
<dd><p>Propose a new point given <code class="docutils literal notranslate"><span class="pre">y</span></code> using the random number
generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>y</strong> – Vector-like array; the current position</p></li>
<li><p><strong>rng</strong> – <p>State of a random number generator like numpy.random.mtrand</p>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must return a numpy array of N samples from:</p>
<ul>
<li><p><strong>rng.normal(0,1,N)</strong>: standard gaussian distribution</p></li>
</ul>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.gauss.LocalGauss.update">
<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.gauss.LocalGauss.update" title="Permalink to this definition"></a></dt>
<dd><p>Re-initialize the proposal with a new covariance matrix.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>sigma</strong> – Matrix-like array; the new covariance-matrix.</p>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>On <code class="docutils literal notranslate"><span class="pre">LinAlgError</span></code>, the old covariance matrix is plugged in
and the proposal remains in a valid state.</p>
</div>
</dd></dl>
</dd></dl>
</section>
<section id="module-pypmc.density.student_t">
<span id="studentt"></span><h3><span class="section-number">6.1.2. </span>StudentT<a class="headerlink" href="#module-pypmc.density.student_t" title="Permalink to this heading"></a></h3>
<p>Collect Student’s t probability densities</p>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.student_t.LocalStudentT">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.student_t.</span></span><span class="sig-name descname"><span class="pre">LocalStudentT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">double</span> <span class="pre">dof</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.LocalStudentT" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pypmc.density.gauss.LocalGauss" title="pypmc.density.gauss.LocalGauss"><code class="xref py py-class docutils literal notranslate"><span class="pre">LocalGauss</span></code></a></p>
<p>A multivariate local Student’s t density with redefinable covariance.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>sigma</strong> – Matrix-like array; the covariance-matrix</p></li>
<li><p><strong>dof</strong> – Float; the degrees of freedom</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.LocalStudentT.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.LocalStudentT.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> – Vector-like array; the proposed point.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.LocalStudentT.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">_np.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.LocalStudentT.propose" title="Permalink to this definition"></a></dt>
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span></dt>
<dd><p>Propose N points using the random number generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>N</strong> – Integer; the number of random points to be proposed</p></li>
<li><p><strong>rng</strong> – <p>State of a random number generator like <code class="docutils literal notranslate"><span class="pre">numpy.random.mtrand</span></code></p>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must return</p>
<ul>
<li><p>a numpy array of N samples from
<strong>rng.normal(0,1,N)</strong>: standard gaussian distribution</p></li>
<li><p>sample as float from
<strong>rng.chisquare(degree_of_freedom)</strong>: any chi-squared
distribution</p></li>
</ul>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.student_t.StudentT">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.student_t.</span></span><span class="sig-name descname"><span class="pre">StudentT</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">double</span> <span class="pre">dof</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.StudentT" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pypmc.density.base.ProbabilityDensity" title="pypmc.density.base.ProbabilityDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProbabilityDensity</span></code></a></p>
<p>A Student’s t probability density. Can be used as a component in
MixtureDensities.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mu</strong> – Vector-like array; the gaussian’s mean <span class="math notranslate nohighlight">\(\mu\)</span></p></li>
<li><p><strong>sigma</strong> – Matrix-like array; the gaussian’s covariance matrix <span class="math notranslate nohighlight">\(\Sigma\)</span></p></li>
<li><p><strong>dof</strong> – Float; the degrees of freedom <span class="math notranslate nohighlight">\(\nu\)</span></p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.StudentT.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.StudentT.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> – Vector-like array; the proposed point.</p>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.StudentT.multi_evaluate">
<span class="sig-name descname"><span class="pre">multi_evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">out=None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.StudentT.multi_evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x))
for each row in x.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Matrix-like array; the proposed points. Expect i-th accessible
as <code class="docutils literal notranslate"><span class="pre">x[i]</span></code>.</p></li>
<li><p><strong>out</strong> – Vector-like array, length==``len(x)``, optional; If provided,
the output is written into this array.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.StudentT.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">int</span> <span class="pre">N=1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng=_np.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.StudentT.propose" title="Permalink to this definition"></a></dt>
<dt class="sig sig-object py">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">None</span></span></span></dt>
<dd><p>Propose N points using the random number generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>N</strong> – Integer; the number of random points to be proposed</p></li>
<li><p><strong>rng</strong> – <p>State of a random number generator like <code class="docutils literal notranslate"><span class="pre">numpy.random.mtrand</span></code></p>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must meet the requirements of
<a class="reference internal" href="#pypmc.density.student_t.LocalStudentT.propose" title="pypmc.density.student_t.LocalStudentT.propose"><code class="xref py py-meth docutils literal notranslate"><span class="pre">LocalStudentT.propose</span></code></a>.</p>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.student_t.StudentT.update">
<span class="sig-name descname"><span class="pre">update</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">mu</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">sigma</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">double</span> <span class="pre">dof</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.student_t.StudentT.update" title="Permalink to this definition"></a></dt>
<dd><p>Re-initialize the density with new mean, covariance matrix and
degrees of freedom.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>mu</strong> – Vector-like array; the gaussian’s mean <span class="math notranslate nohighlight">\(\mu\)</span></p></li>
<li><p><strong>sigma</strong> – Matrix-like array; the gaussian’s covariance matrix
<span class="math notranslate nohighlight">\(\Sigma\)</span></p></li>
<li><p><strong>dof</strong> – Float; the degrees of freedom <span class="math notranslate nohighlight">\(\nu\)</span></p></li>
</ul>
</dd>
</dl>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>On <code class="docutils literal notranslate"><span class="pre">LinAlgError</span></code>, the old <code class="docutils literal notranslate"><span class="pre">mu</span></code>, <code class="docutils literal notranslate"><span class="pre">sigma</span></code>, and <code class="docutils literal notranslate"><span class="pre">dof</span></code>
are plugged in and the proposal remains in a valid state.</p>
</div>
</dd></dl>
</dd></dl>
</section>
<section id="module-pypmc.density.mixture">
<span id="mixture"></span><h3><span class="section-number">6.1.3. </span>Mixture<a class="headerlink" href="#module-pypmc.density.mixture" title="Permalink to this heading"></a></h3>
<p>Collect mixture probability densities</p>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.density.mixture.</span></span><span class="sig-name descname"><span class="pre">MixtureDensity</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">components</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity" title="Permalink to this definition"></a></dt>
<dd><p>Bases: <a class="reference internal" href="#pypmc.density.base.ProbabilityDensity" title="pypmc.density.base.ProbabilityDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">ProbabilityDensity</span></code></a></p>
<p>Base class for mixture probability densities.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>components</strong> – Iterable of ProbabilityDensities; the mixture’s components</p></li>
<li><p><strong>weights</strong> – Iterable of floats; the weights of the components
(will be normalized automatically during initialization)</p></li>
</ul>
</dd>
</dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.evaluate">
<span class="sig-name descname"><span class="pre">evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">individual</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate log of the density to propose <code class="docutils literal notranslate"><span class="pre">x</span></code>, namely log(q(x)).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – Vector-like array; the proposed point.</p></li>
<li><p><strong>individual</strong> – bool; If true, return the evaluation of each component at <code class="docutils literal notranslate"><span class="pre">x</span></code> as
an array.</p></li>
</ul>
</dd>
</dl>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p>This function assumes that the weights are normalized, i.e.
that <code class="docutils literal notranslate"><span class="pre">self.normalized()</span></code> returns <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.multi_evaluate">
<span class="sig-name descname"><span class="pre">multi_evaluate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">out=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">ndarray</span> <span class="pre">individual=None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">components=None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.multi_evaluate" title="Permalink to this definition"></a></dt>
<dd><p>Evaluate density at all points in <code class="docutils literal notranslate"><span class="pre">x</span></code> for all components
specified in <code class="docutils literal notranslate"><span class="pre">components</span></code> and return in <code class="docutils literal notranslate"><span class="pre">individual</span></code>.
Return log(q(x)) for each point (if <code class="docutils literal notranslate"><span class="pre">components</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code>).</p>
<p>Use <code class="docutils literal notranslate"><span class="pre">individual</span></code> if you need the density at <code class="docutils literal notranslate"><span class="pre">x</span></code> for each component
and you want to compute it only once to increase efficiency.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x</strong> – (N x D) array; one D-dim. sample per row.</p></li>
<li><p><strong>out</strong> – (N) array, optional; write output into this array (if
<code class="docutils literal notranslate"><span class="pre">components</span></code> is <code class="docutils literal notranslate"><span class="pre">None</span></code>).</p></li>
<li><p><strong>individual</strong> – (N x K) array; density of k-th component at the n-th sample.</p></li>
<li><p><strong>components</strong> – Iterable of integers; calculate <code class="docutils literal notranslate"><span class="pre">individual</span></code> for these
components only.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.normalize">
<span class="sig-name descname"><span class="pre">normalize</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.normalize" title="Permalink to this definition"></a></dt>
<dd><p>Normalize the component weights to sum up to 1.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.normalized">
<span class="sig-name descname"><span class="pre">normalized</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.normalized" title="Permalink to this definition"></a></dt>
<dd><p>Check if the component weights are normalized.</p>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.propose">
<span class="sig-name descname"><span class="pre">propose</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">N</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">_np.random.mtrand</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">trace</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">shuffle</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.propose" title="Permalink to this definition"></a></dt>
<dd><p>Propose N points using the random number generator <code class="docutils literal notranslate"><span class="pre">rng</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>N</strong> – Integer; the number of random points to be proposed</p></li>
<li><p><strong>rng</strong> – State of a random number generator like numpy.random.mtrand</p></li>
<li><p><strong>shuffle</strong> – bool; if True (default), the samples are disordered. Otherwise,
the samples are ordered by the components.</p></li>
<li><p><strong>trace</strong> – bool; if True, return the proposed samples and an array containing
the number of the component responsible for each sample, otherwise
just return the samples.</p></li>
</ul>
</dd>
</dl>
<div class="admonition important">
<p class="admonition-title">Important</p>
<dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">rng</span></code> must:</dt><dd><ul class="simple">
<li><p>return a numpy array of N samples from the multinomial
distribution with probabilities <code class="docutils literal notranslate"><span class="pre">pvals</span></code> when calling
<strong>rng.multinomial(N, pvals)</strong></p></li>
<li><p>shuffle an <code class="docutils literal notranslate"><span class="pre">array</span></code> in place when calling <strong>rng.shuffle(array)</strong></p></li>
</ul>
</dd>
</dl>
</div>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p>This function assumes that the weights are normalized, i.e.
that <code class="docutils literal notranslate"><span class="pre">self.normalized()</span></code> returns <code class="docutils literal notranslate"><span class="pre">True</span></code>.</p>
</div>
</dd></dl>
<dl class="py method">
<dt class="sig sig-object py" id="pypmc.density.mixture.MixtureDensity.prune">
<span class="sig-name descname"><span class="pre">prune</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">self</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">threshold</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.0</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.MixtureDensity.prune" title="Permalink to this definition"></a></dt>
<dd><p>Remove components with weight less or equal <code class="docutils literal notranslate"><span class="pre">threshold</span></code>.
Return list of removed components and weights in the form:
[(index, component, weight), …].</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>threshold</strong> – Float; components with lower weight are deleted</p>
</dd>
</dl>
</dd></dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.density.mixture.create_gaussian_mixture">
<span class="sig-prename descclassname"><span class="pre">pypmc.density.mixture.</span></span><span class="sig-name descname"><span class="pre">create_gaussian_mixture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">means</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">covs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.create_gaussian_mixture" title="Permalink to this definition"></a></dt>
<dd><p>Create a <a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a> with Gaussian (<a class="reference internal" href="#pypmc.density.gauss.Gauss" title="pypmc.density.gauss.Gauss"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gauss</span></code></a>)
components. The output can be used for the clustering algorithms.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#pypmc.density.mixture.recover_gaussian_mixture" title="pypmc.density.mixture.recover_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_gaussian_mixture</span></code></a>, <a class="reference internal" href="#pypmc.density.mixture.create_t_mixture" title="pypmc.density.mixture.create_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_t_mixture</span></code></a>,
<a class="reference internal" href="#pypmc.density.mixture.recover_t_mixture" title="pypmc.density.mixture.recover_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_t_mixture</span></code></a></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>means</strong> – Vector-like array; the means of the Gaussian mixture</p></li>
<li><p><strong>covs</strong> – 3d-matrix-like array; the covariances of the Gaussian mixture.
<code class="docutils literal notranslate"><span class="pre">cov[i]</span></code> will be interpreted as the i’th covariance matrix.</p></li>
<li><p><strong>weights</strong> – <p>Vector-like array, optional; the component weights. If not
provided all components will get equal weight.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The weights will automatically be normalized.</p>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.density.mixture.create_t_mixture">
<span class="sig-prename descclassname"><span class="pre">pypmc.density.mixture.</span></span><span class="sig-name descname"><span class="pre">create_t_mixture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">means</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">covs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">dofs</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.create_t_mixture" title="Permalink to this definition"></a></dt>
<dd><p>Create a <a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a> with Student t
(<a class="reference internal" href="#pypmc.density.student_t.StudentT" title="pypmc.density.student_t.StudentT"><code class="xref py py-class docutils literal notranslate"><span class="pre">StudentT</span></code></a>) components. The output can be used for the
clustering algorithms.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#pypmc.density.mixture.recover_t_mixture" title="pypmc.density.mixture.recover_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_t_mixture</span></code></a>, <a class="reference internal" href="#pypmc.density.mixture.create_gaussian_mixture" title="pypmc.density.mixture.create_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_gaussian_mixture</span></code></a>,
<a class="reference internal" href="#pypmc.density.mixture.recover_gaussian_mixture" title="pypmc.density.mixture.recover_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_gaussian_mixture</span></code></a></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>means</strong> – Vector-like array; the means of the mixture</p></li>
<li><p><strong>covs</strong> – 3d-matrix-like array; the covariances of the mixture. <code class="docutils literal notranslate"><span class="pre">cov[i]</span></code>
will be interpreted as the i’th covariance matrix.</p></li>
<li><p><strong>dofs</strong> – Vector-like array; the degrees of freedom</p></li>
<li><p><strong>weights</strong> – <p>Vector-like array, optional; the component weights. If not
provided all components will get equal weight.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The weights will automatically be normalized.</p>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.density.mixture.recover_gaussian_mixture">
<span class="sig-prename descclassname"><span class="pre">pypmc.density.mixture.</span></span><span class="sig-name descname"><span class="pre">recover_gaussian_mixture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mixture</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.recover_gaussian_mixture" title="Permalink to this definition"></a></dt>
<dd><p>Extract the means, covariances and component weights from a
<a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a>.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#pypmc.density.mixture.create_gaussian_mixture" title="pypmc.density.mixture.create_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_gaussian_mixture</span></code></a>, <a class="reference internal" href="#pypmc.density.mixture.create_t_mixture" title="pypmc.density.mixture.create_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_t_mixture</span></code></a>,
<a class="reference internal" href="#pypmc.density.mixture.recover_t_mixture" title="pypmc.density.mixture.recover_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_t_mixture</span></code></a></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>mixture</strong> – <a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a> with Gaussian (<a class="reference internal" href="#pypmc.density.gauss.Gauss" title="pypmc.density.gauss.Gauss"><code class="xref py py-class docutils literal notranslate"><span class="pre">Gauss</span></code></a>)
components; the mixture to be decomposed.</p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.density.mixture.recover_t_mixture">
<span class="sig-prename descclassname"><span class="pre">pypmc.density.mixture.</span></span><span class="sig-name descname"><span class="pre">recover_t_mixture</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">mixture</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#pypmc.density.mixture.recover_t_mixture" title="Permalink to this definition"></a></dt>
<dd><p>Extract the means, covariances, degrees of freedom and component
weights from a <a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a>.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#pypmc.density.mixture.create_t_mixture" title="pypmc.density.mixture.create_t_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_t_mixture</span></code></a>, <a class="reference internal" href="#pypmc.density.mixture.create_gaussian_mixture" title="pypmc.density.mixture.create_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">create_gaussian_mixture</span></code></a>,
<a class="reference internal" href="#pypmc.density.mixture.recover_gaussian_mixture" title="pypmc.density.mixture.recover_gaussian_mixture"><code class="xref py py-func docutils literal notranslate"><span class="pre">recover_gaussian_mixture</span></code></a></p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>mixture</strong> – <a class="reference internal" href="#pypmc.density.mixture.MixtureDensity" title="pypmc.density.mixture.MixtureDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">MixtureDensity</span></code></a> with Student t (<a class="reference internal" href="#pypmc.density.student_t.StudentT" title="pypmc.density.student_t.StudentT"><code class="xref py py-class docutils literal notranslate"><span class="pre">StudentT</span></code></a>)
components; the mixture to be decomposed.</p>
</dd>
</dl>
</dd></dl>
</section>
</section>
<section id="module-pypmc.sampler">
<span id="sampler"></span><h2><span class="section-number">6.2. </span>Sampler<a class="headerlink" href="#module-pypmc.sampler" title="Permalink to this heading"></a></h2>
<p>Collect the sampler modules</p>
<section id="module-pypmc.sampler.markov_chain">
<span id="markov-chain"></span><h3><span class="section-number">6.2.1. </span>Markov Chain<a class="headerlink" href="#module-pypmc.sampler.markov_chain" title="Permalink to this heading"></a></h3>
<p>Collect Markov Chain</p>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.sampler.markov_chain.MarkovChain">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.sampler.markov_chain.</span></span><span class="sig-name descname"><span class="pre">MarkovChain</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">target</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">proposal</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">indicator</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/markov_chain.html#MarkovChain"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.markov_chain.MarkovChain" title="Permalink to this definition"></a></dt>
<dd><p>A Markov chain to generate samples from the target density.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>target</strong> – The target density. Must be a function accepting a 1d numpy
array and returning a float, namely <span class="math notranslate nohighlight">\(\log(P(x))\)</span>,
the log of the target <cite>P</cite>.</p></li>
<li><p><strong>proposal</strong> – <p>The proposal density <cite>q</cite>.
Should be of type <a class="reference internal" href="#pypmc.density.base.LocalDensity" title="pypmc.density.base.LocalDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">pypmc.density.base.LocalDensity</span></code></a>.</p>
<div class="admonition hint">
<p class="admonition-title">Hint</p>
<p>If your proposal density is symmetric, define the member
variable <code class="docutils literal notranslate"><span class="pre">proposal.symmetric</span> <span class="pre">=</span> <span class="pre">True</span></code>. This will omit calls
to proposal.evaluate in the Metropolis-Hastings steps.</p>
</div>
</p></li>
<li><p><strong>start</strong> – The starting point of the Markov chain. (numpy array)</p></li>
<li><p><strong>indicator</strong> – <p>The indicator function receives a numpy array and returns bool.
The target is only called if indicator(proposed_point)
returns True, otherwise the proposed point is rejected
without call to target.
Use this function to specify the support of the target.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#module-pypmc.tools.indicator" title="pypmc.tools.indicator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">pypmc.tools.indicator</span></code></a></p>
</div>
</p></li>
<li><p><strong>prealloc</strong> – <p>Integer; the number of Markov chain samples for which memory in
<code class="docutils literal notranslate"><span class="pre">self.samples</span></code> is allocated. If more memory is needed, it will
be allocated on demand.</p>
<div class="admonition hint">
<p class="admonition-title">Hint</p>
<p>Preallocating memory can speed up the calculation, in
particular if it is known in advance how long the chains
are run.</p>
</div>
</p></li>
<li><p><strong>save_target_values</strong> – Bool; if <code class="docutils literal notranslate"><span class="pre">True</span></code>, store the evaluated <code class="docutils literal notranslate"><span class="pre">target</span></code> at every visited
point in <code class="docutils literal notranslate"><span class="pre">self.target_values</span></code></p></li>
<li><p><strong>rng</strong> – <p>The rng passed to the proposal when calling proposal.propose</p>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must return a sample from the uniform distribution
in [0,1) when calling <strong>rng.rand()</strong></p>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must also fulfill the requirements of your proposal
<a class="reference internal" href="#pypmc.density.base.LocalDensity.propose" title="pypmc.density.base.LocalDensity.propose"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pypmc.density.base.LocalDensity.propose</span></code></a></p>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py class">
<dt class="sig sig-object py" id="pypmc.sampler.markov_chain.AdaptiveMarkovChain">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">pypmc.sampler.markov_chain.</span></span><span class="sig-name descname"><span class="pre">AdaptiveMarkovChain</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">target</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">proposal</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">start</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">indicator</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">rng</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">numpy.random.mtrand</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/markov_chain.html#AdaptiveMarkovChain"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.markov_chain.AdaptiveMarkovChain" title="Permalink to this definition"></a></dt>
<dd><p>A Markov chain with proposal covariance adaptation as in <a class="reference internal" href="references.html#hst01" id="id1"><span>[HST01]</span></a> to generate samples from the target density.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>target</strong> – The target density. Must be a function accepting a 1d numpy
array and returning a float, namely <span class="math notranslate nohighlight">\(\log(P(x))\)</span>,
the log of the target <cite>P</cite>.</p></li>
<li><p><strong>proposal</strong> – <p>The proposal density <cite>q</cite>.
Should be of type <a class="reference internal" href="#pypmc.density.base.LocalDensity" title="pypmc.density.base.LocalDensity"><code class="xref py py-class docutils literal notranslate"><span class="pre">pypmc.density.base.LocalDensity</span></code></a>.</p>
<div class="admonition hint">
<p class="admonition-title">Hint</p>
<p>If your proposal density is symmetric, define the member
variable <code class="docutils literal notranslate"><span class="pre">proposal.symmetric</span> <span class="pre">=</span> <span class="pre">True</span></code>. This will omit calls
to proposal.evaluate in the Metropolis-Hastings steps.</p>
</div>
</p></li>
<li><p><strong>start</strong> – The starting point of the Markov chain. (numpy array)</p></li>
<li><p><strong>indicator</strong> – <p>The indicator function receives a numpy array and returns bool.
The target is only called if indicator(proposed_point)
returns True, otherwise the proposed point is rejected
without call to target.
Use this function to specify the support of the target.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#module-pypmc.tools.indicator" title="pypmc.tools.indicator"><code class="xref py py-mod docutils literal notranslate"><span class="pre">pypmc.tools.indicator</span></code></a></p>
</div>
</p></li>
<li><p><strong>prealloc</strong> – <p>Integer; the number of Markov chain samples for which memory in
<code class="docutils literal notranslate"><span class="pre">self.samples</span></code> is allocated. If more memory is needed, it will
be allocated on demand.</p>
<div class="admonition hint">
<p class="admonition-title">Hint</p>
<p>Preallocating memory can speed up the calculation, in
particular if it is known in advance how long the chains
are run.</p>
</div>
</p></li>
<li><p><strong>save_target_values</strong> – Bool; if <code class="docutils literal notranslate"><span class="pre">True</span></code>, store the evaluated <code class="docutils literal notranslate"><span class="pre">target</span></code> at every visited
point in <code class="docutils literal notranslate"><span class="pre">self.target_values</span></code></p></li>
<li><p><strong>rng</strong> – <p>The rng passed to the proposal when calling proposal.propose</p>
<div class="admonition important">
<p class="admonition-title">Important</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must return a sample from the uniform distribution
in [0,1) when calling <strong>rng.rand()</strong></p>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><code class="docutils literal notranslate"><span class="pre">rng</span></code> must also fulfill the requirements of your proposal
<a class="reference internal" href="#pypmc.density.base.LocalDensity.propose" title="pypmc.density.base.LocalDensity.propose"><code class="xref py py-meth docutils literal notranslate"><span class="pre">pypmc.density.base.LocalDensity.propose</span></code></a></p>
</div>
</p></li>
</ul>
</dd>
</dl>
</dd></dl>
</section>
<section id="module-pypmc.sampler.importance_sampling">
<span id="importance-sampling"></span><h3><span class="section-number">6.2.2. </span>Importance Sampling<a class="headerlink" href="#module-pypmc.sampler.importance_sampling" title="Permalink to this heading"></a></h3>
<p>Some useful tools for importance sampling. The main class is
<a class="reference internal" href="#pypmc.sampler.importance_sampling.ImportanceSampler" title="pypmc.sampler.importance_sampling.ImportanceSampler"><code class="xref py py-class docutils literal notranslate"><span class="pre">ImportanceSampler</span></code></a> and there are some utility functions.</p>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.sampler.importance_sampling.calculate_covariance">
<span class="sig-prename descclassname"><span class="pre">pypmc.sampler.importance_sampling.</span></span><span class="sig-name descname"><span class="pre">calculate_covariance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/importance_sampling.html#calculate_covariance"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.importance_sampling.calculate_covariance" title="Permalink to this definition"></a></dt>
<dd><p>Calculates the covariance matrix of weighted samples (like the output of an
importance-sampling run).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>samples</strong> – Matrix-like numpy array; the samples to be used.</p></li>
<li><p><strong>weights</strong> – Vector-like numpy array; the (unnormalized) importance weights.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.sampler.importance_sampling.calculate_expectation">
<span class="sig-prename descclassname"><span class="pre">pypmc.sampler.importance_sampling.</span></span><span class="sig-name descname"><span class="pre">calculate_expectation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/importance_sampling.html#calculate_expectation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.importance_sampling.calculate_expectation" title="Permalink to this definition"></a></dt>
<dd><p>Calculate the expectation value of function <code class="docutils literal notranslate"><span class="pre">f</span></code> using weighted
samples (like the output of an importance-sampling run).</p>
<p>Denoting <span class="math notranslate nohighlight">\(x_n\)</span> as the sample n and <span class="math notranslate nohighlight">\(w_n\)</span> as its (normalized)
weight, the following is returned:</p>
<div class="math notranslate nohighlight">
\[\sum_{n=1}^{N} w_n f(x_n)
\mathrm{\ \ where\ \ } \sum_{n=1}^{N}w_n \overset{!}{=} 1\]</div>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>samples</strong> – Matrix-like numpy array; the samples to be used.</p></li>
<li><p><strong>weights</strong> – Vector-like numpy array; the (unnormalized) importance weights.</p></li>
<li><p><strong>f</strong> – Callable, the function to be evaluated.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.sampler.importance_sampling.calculate_mean">
<span class="sig-prename descclassname"><span class="pre">pypmc.sampler.importance_sampling.</span></span><span class="sig-name descname"><span class="pre">calculate_mean</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/importance_sampling.html#calculate_mean"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.importance_sampling.calculate_mean" title="Permalink to this definition"></a></dt>
<dd><p>Calculate the mean of weighted samples (like the output of an
importance-sampling run).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>samples</strong> – Matrix-like numpy array; the samples to be used.</p></li>
<li><p><strong>weights</strong> – Vector-like numpy array; the (unnormalized) importance weights.</p></li>
</ul>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="pypmc.sampler.importance_sampling.combine_weights">
<span class="sig-prename descclassname"><span class="pre">pypmc.sampler.importance_sampling.</span></span><span class="sig-name descname"><span class="pre">combine_weights</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">samples</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">weights</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">proposals</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/pypmc/sampler/importance_sampling.html#combine_weights"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#pypmc.sampler.importance_sampling.combine_weights" title="Permalink to this definition"></a></dt>
<dd><p>Calculate the <cite>deterministic mixture weights</cite> according to
<a class="reference internal" href="references.html#cor-12" id="id2"><span>[Cor+12]</span></a> given <code class="docutils literal notranslate"><span class="pre">samples</span></code>, standard <code class="docutils literal notranslate"><span class="pre">weights</span></code> and their <code class="docutils literal notranslate"><span class="pre">proposals</span></code> for a
number of steps in which importance samples are computed for the same target
density but different proposals.</p>
<p>Return the weights as a <a class="reference internal" href="#pypmc.tools.History" title="pypmc.tools.History"><code class="xref py py-class docutils literal notranslate"><span class="pre">pypmc.tools.History</span></code></a> such that the
weights for each proposal are easily accessible.</p>
<dl class="field-list simple">