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<section id="sampling-configuration-guide" class="level1">
<h1>Sampling Configuration Guide</h1>
<p>This guide covers the configuration options for <code>nutpie.sample</code> and provides practical advice for tuning your sampler. We’ll start with basic usage and move to advanced topics like mass matrix adaptation.</p>
<section id="quick-start" class="level2">
<h2 class="anchored" data-anchor-id="quick-start">Quick Start</h2>
<p>For most models, don’t think too much about the options of the sampler, and just use the defaults. Most sampling problems can’t easily be solved by changing the sampler, most of the time they require model changes. So in most cases, simply use</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(compiled_model)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="core-sampling-parameters" class="level2">
<h2 class="anchored" data-anchor-id="core-sampling-parameters">Core Sampling Parameters</h2>
<section id="drawing-samples" class="level3">
<h3 class="anchored" data-anchor-id="drawing-samples">Drawing Samples</h3>
<div class="sourceCode" id="cb2"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a> draws<span class="op">=</span><span class="dv">1000</span>, <span class="co"># Number of post-warmup draws per chain</span></span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a> tune<span class="op">=</span><span class="dv">500</span>, <span class="co"># Number of warmup draws for adaptation</span></span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> chains<span class="op">=</span><span class="dv">6</span>, <span class="co"># Number of independent chains</span></span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a> cores<span class="op">=</span><span class="va">None</span>, <span class="co"># Number chains that are allowed to run simultainiously</span></span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> seed<span class="op">=</span><span class="dv">12345</span> <span class="co"># Random seed for reproducibility</span></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>The number of draws affects both accuracy and computational cost: - Too few draws (< 500) may not capture the posterior well - Too many draws (> 10000) may waste computation time</p>
<p>If a model is sampling without divergences, but with effective sample sizes that are not as large as necessary to accieve the markov-error for your estimates, you can increase the number of chains and/or draws.</p>
<p>If the effective sample size is much smaller than the number of draws, you might want to consider reparameterizing the model instead, to for instance remove posterior correlations.</p>
</section>
</section>
<section id="sampler-diagnostics" class="level2">
<h2 class="anchored" data-anchor-id="sampler-diagnostics">Sampler Diagnostics</h2>
<p>You can enable more detailed diagnostics when troubleshooting:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a> save_warmup<span class="op">=</span><span class="va">True</span>, <span class="co"># Keep warmup draws, default is True</span></span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a> store_divergences<span class="op">=</span><span class="va">True</span>, <span class="co"># Track divergent transitions</span></span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a> store_unconstrained<span class="op">=</span><span class="va">True</span>, <span class="co"># Store transformed parameters</span></span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> store_gradient<span class="op">=</span><span class="va">True</span>, <span class="co"># Store gradient information</span></span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a> store_mass_matrix<span class="op">=</span><span class="va">True</span> <span class="co"># Track mass matrix adaptation</span></span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>For each of the <code>store_*</code> arguments, additional arrays will be availbale in the <code>trace.sample_stats</code>.</p>
</section>
<section id="non-blocking-sampling" class="level2">
<h2 class="anchored" data-anchor-id="non-blocking-sampling">Non-blocking sampling</h2>
<section id="settings-for-hmc-and-nuts" class="level3">
<h3 class="anchored" data-anchor-id="settings-for-hmc-and-nuts">Settings for HMC and NUTS</h3>
<div class="sourceCode" id="cb4"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a> target_accept<span class="op">=</span><span class="fl">0.8</span>, <span class="co"># Target acceptance rate</span></span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a> maxdepth<span class="op">=</span><span class="dv">10</span> <span class="co"># Maximum tree depth</span></span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a> max_energy_error<span class="op">=</span><span class="dv">1000</span> <span class="co"># Error at witch to count the trajectory as a divergent transition</span></span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>The <code>target_accept</code> parameter implicitly controls the step size of the leapfrog steps in the HMC sampler. During tuning, the sampler will try to choose a step size, such that the acceptance statistic is <code>target_accept</code>. It has to be between 0 and 1.</p>
<p>The default is 0.8. Larger values will increase the computational cost, but might avoid divergences during sampling. In many diverging models increasing <code>target_accept</code> will only make divergences less frequent however, and not solve the underlying problem.</p>
<p>Lowering the maximum energy error to for instance 10 will often increase the number of divergences, and make it easier to diagnose their cause. With lower value the divergences often are reported closer to the critical points in the parameter space, where the model is most likely to diverge.</p>
</section>
</section>
<section id="mass-matrix-adaptation" class="level2">
<h2 class="anchored" data-anchor-id="mass-matrix-adaptation">Mass Matrix Adaptation</h2>
<p>Nutpie offers several strategies for adapting the mass matrix, which determines how the sampler navigates the parameter space.</p>
<section id="standard-adaptation" class="level3">
<h3 class="anchored" data-anchor-id="standard-adaptation">Standard Adaptation</h3>
<p>By setting <code>use_grad_based_mass_matrix=False</code>, the sampling algorithm will more closely resemble the algorithm in Stan and PyMC. Usually, this will result in less efficient sampling, but the total number of effective samples is sometimes higher. If this is set to <code>True</code> (the default), nutpie will use diagonal mass matrix estimates that are based on the posterior draws and the scores at those positions.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a> use_grad_based_mass_matrix<span class="op">=</span><span class="va">False</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="low-rank-updates" class="level3">
<h3 class="anchored" data-anchor-id="low-rank-updates">Low-Rank Updates</h3>
<p>For models with strong parameter correlations you can enable a low rank modified mass matrix. The <code>mass_matrix_gamma</code> parameter is a regularization parameter. More regularization will lead to a smaller effect of the low-rank components, but might work better for hiegher dimensional problems.</p>
<p><code>mass_matrix_eigval_cutoff</code> should be greater than one, and controls how large an eigenvalue of the full mass matrix has to be, to be included into the low-rank mass matirx.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a> low_rank_modified_mass_matrix<span class="op">=</span><span class="va">True</span>,</span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a> mass_matrix_eigval_cutoff<span class="op">=</span><span class="dv">3</span>,</span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a> mass_matrix_gamma<span class="op">=</span><span class="fl">1e-5</span></span>
<span id="cb6-6"><a href="#cb6-6" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="experimental-features" class="level3">
<h3 class="anchored" data-anchor-id="experimental-features">Experimental Features</h3>
<p><code>trasform_adapt</code> is an experimental feature that allows sampling from many posteriors, where current methods diverge. It is described in more detail <a href="./nf-adapt.html">here</a>.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a> transform_adapt<span class="op">=</span><span class="va">True</span> <span class="co"># Experimental reparameterization</span></span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
</section>
<section id="progress-monitoring" class="level2">
<h2 class="anchored" data-anchor-id="progress-monitoring">Progress Monitoring</h2>
<p>Customize the sampling progress display:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a> model,</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a> progress_bar<span class="op">=</span><span class="va">True</span>,</span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a> progress_rate<span class="op">=</span><span class="dv">500</span>, <span class="co"># Update every 500ms</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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