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<li><a href="#compiler-toolchain" id="toc-compiler-toolchain" class="nav-link" data-scroll-target="#compiler-toolchain">Compiler Toolchain</a></li>
<li><a href="#defining-and-sampling-a-simple-model" id="toc-defining-and-sampling-a-simple-model" class="nav-link" data-scroll-target="#defining-and-sampling-a-simple-model">Defining and Sampling a Simple Model</a>
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<h1 class="title">Usage with Stan models</h1>
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<p>This document shows how to use <code>nutpie</code> with Stan models. We will use the <code>nutpie</code> package to define a simple model and sample from it using Stan.</p>
<section id="installation" class="level2">
<h2 class="anchored" data-anchor-id="installation">Installation</h2>
<p>For Stan, it is more common to use <code>pip</code> or <code>uv</code> to install the necessary packages. However, <code>conda</code> is also an option if you prefer.</p>
<p>To install using <code>pip</code>:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="ex">pip</span> install <span class="st">"nutpie[stan]"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>To install using <code>uv</code>:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="ex">uv</span> add <span class="st">"nutpie[stan]"</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<p>To install using <code>conda</code>:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode bash code-with-copy"><code class="sourceCode bash"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="ex">conda</span> install <span class="at">-c</span> conda-forge nutpie</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</section>
<section id="compiler-toolchain" class="level2">
<h2 class="anchored" data-anchor-id="compiler-toolchain">Compiler Toolchain</h2>
<p>Stan requires a compiler toolchain to be installed on your system. This is necessary for compiling the Stan models. You can find detailed instructions for setting up the compiler toolchain in the <a href="https://mc-stan.org/docs/cmdstan-guide/installation.html#cpp-toolchain">CmdStan Guide</a>.</p>
<p>Additionally, since Stan uses Intel’s Threading Building Blocks (TBB) for parallelism, you might need to set the <code>TBB_CXX_TYPE</code> environment variable to specify the compiler type. Depending on your system, you can set it to either <code>clang</code> or <code>gcc</code>. For example:</p>
<div id="8f4ef971" class="cell" data-execution_count="1">
<div class="sourceCode cell-code" 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><span class="im">import</span> os</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>os.environ[<span class="st">"TBB_CXX_TYPE"</span>] <span class="op">=</span> <span class="st">"clang"</span> <span class="co"># or 'gcc'</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Make sure to set this environment variable before compiling your Stan models to ensure proper configuration.</p>
</section>
<section id="defining-and-sampling-a-simple-model" class="level2">
<h2 class="anchored" data-anchor-id="defining-and-sampling-a-simple-model">Defining and Sampling a Simple Model</h2>
<p>We will define a simple Bayesian model using Stan and sample from it using <code>nutpie</code>.</p>
<section id="model-definition" class="level3">
<h3 class="anchored" data-anchor-id="model-definition">Model Definition</h3>
<p>In your Python script or Jupyter notebook, add the following code:</p>
<div id="2cded72e" class="cell" data-execution_count="2">
<div class="sourceCode cell-code" 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><span class="im">import</span> nutpie</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>model_code <span class="op">=</span> <span class="st">"""</span></span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="st">data {</span></span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a><span class="st"> int<lower=0> N;</span></span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a><span class="st"> vector[N] y;</span></span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb5-8"><a href="#cb5-8" aria-hidden="true" tabindex="-1"></a><span class="st">parameters {</span></span>
<span id="cb5-9"><a href="#cb5-9" aria-hidden="true" tabindex="-1"></a><span class="st"> real mu;</span></span>
<span id="cb5-10"><a href="#cb5-10" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb5-11"><a href="#cb5-11" aria-hidden="true" tabindex="-1"></a><span class="st">model {</span></span>
<span id="cb5-12"><a href="#cb5-12" aria-hidden="true" tabindex="-1"></a><span class="st"> mu ~ normal(0, 1);</span></span>
<span id="cb5-13"><a href="#cb5-13" aria-hidden="true" tabindex="-1"></a><span class="st"> y ~ normal(mu, 1);</span></span>
<span id="cb5-14"><a href="#cb5-14" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb5-15"><a href="#cb5-15" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span>
<span id="cb5-16"><a href="#cb5-16" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb5-17"><a href="#cb5-17" aria-hidden="true" tabindex="-1"></a>compiled_model <span class="op">=</span> nutpie.compile_stan_model(code<span class="op">=</span>model_code)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
</section>
<section id="sampling" class="level3">
<h3 class="anchored" data-anchor-id="sampling">Sampling</h3>
<p>We can now compile the model and sample from it:</p>
<div id="60b965bf" class="cell" data-execution_count="3">
<div class="sourceCode cell-code" 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>compiled_model_with_data <span class="op">=</span> compiled_model.with_data(N<span class="op">=</span><span class="dv">3</span>, y<span class="op">=</span>[<span class="dv">1</span>, <span class="dv">2</span>, <span class="dv">3</span>])</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(compiled_model_with_data)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
<style>
:root {
--column-width-1: 40%; /* Progress column width */
--column-width-2: 15%; /* Chain column width */
--column-width-3: 15%; /* Divergences column width */
--column-width-4: 15%; /* Step Size column width */
--column-width-5: 15%; /* Gradients/Draw column width */
}
.nutpie {
max-width: 800px;
margin: 10px auto;
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
//color: #333;
//background-color: #fff;
padding: 10px;
box-shadow: 0 4px 6px rgba(0,0,0,0.1);
border-radius: 8px;
font-size: 14px; /* Smaller font size for a more compact look */
}
.nutpie table {
width: 100%;
border-collapse: collapse; /* Remove any extra space between borders */
}
.nutpie th, .nutpie td {
padding: 8px 10px; /* Reduce padding to make table more compact */
text-align: left;
border-bottom: 1px solid #888;
}
.nutpie th {
//background-color: #f0f0f0;
}
.nutpie th:nth-child(1) { width: var(--column-width-1); }
.nutpie th:nth-child(2) { width: var(--column-width-2); }
.nutpie th:nth-child(3) { width: var(--column-width-3); }
.nutpie th:nth-child(4) { width: var(--column-width-4); }
.nutpie th:nth-child(5) { width: var(--column-width-5); }
.nutpie progress {
width: 100%;
height: 15px; /* Smaller progress bars */
border-radius: 5px;
}
progress::-webkit-progress-bar {
background-color: #eee;
border-radius: 5px;
}
progress::-webkit-progress-value {
background-color: #5cb85c;
border-radius: 5px;
}
progress::-moz-progress-bar {
background-color: #5cb85c;
border-radius: 5px;
}
.nutpie .progress-cell {
width: 100%;
}
.nutpie p strong { font-size: 16px; font-weight: bold; }
@media (prefers-color-scheme: dark) {
.nutpie {
//color: #ddd;
//background-color: #1e1e1e;
box-shadow: 0 4px 6px rgba(0,0,0,0.2);
}
.nutpie table, .nutpie th, .nutpie td {
border-color: #555;
color: #ccc;
}
.nutpie th {
background-color: #2a2a2a;
}
.nutpie progress::-webkit-progress-bar {
background-color: #444;
}
.nutpie progress::-webkit-progress-value {
background-color: #3178c6;
}
.nutpie progress::-moz-progress-bar {
background-color: #3178c6;
}
}
</style>
</div>
<div class="cell-output cell-output-display">
<div class="nutpie">
<p><strong>Sampler Progress</strong></p>
<p>Total Chains: <span id="total-chains">6</span></p>
<p>Active Chains: <span id="active-chains">0</span></p>
<p>
Finished Chains:
<span id="active-chains">6</span>
</p>
<p>Sampling for now</p>
<p>
Estimated Time to Completion:
<span id="eta">now</span>
</p>
<progress id="total-progress-bar" max="8400" value="8400">
</progress>
<table>
<thead>
<tr>
<th>Progress</th>
<th>Draws</th>
<th>Divergences</th>
<th>Step Size</th>
<th>Gradients/Draw</th>
</tr>
</thead>
<tbody id="chain-details">
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.33</td>
<td>3</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.39</td>
<td>1</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.37</td>
<td>3</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.38</td>
<td>1</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.35</td>
<td>3</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>1.33</td>
<td>3</td>
</tr>
</tbody>
</table>
</div>
</div>
</div>
</section>
<section id="using-dimensions" class="level3">
<h3 class="anchored" data-anchor-id="using-dimensions">Using Dimensions</h3>
<p>We’ll use the radon model from <a href="https://mc-stan.org/learn-stan/case-studies/radon_cmdstanpy_plotnine.html">this</a> case-study from the stan documentation, to show how we can use coordinates and dimension names to simplify working with trace objects.</p>
<p>We follow the same data preparation as in the case-study:</p>
<div id="92d854e3" class="cell" data-execution_count="4">
<div class="sourceCode cell-code" 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><span class="im">import</span> pandas <span class="im">as</span> pd</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> numpy <span class="im">as</span> np</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> arviz <span class="im">as</span> az</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> seaborn <span class="im">as</span> sns</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a>home_data <span class="op">=</span> pd.read_csv(</span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a> <span class="st">"https://github.com/pymc-devs/pymc-examples/raw/refs/heads/main/examples/data/srrs2.dat"</span>,</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a> index_col<span class="op">=</span><span class="st">"idnum"</span>,</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>county_data <span class="op">=</span> pd.read_csv(</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a> <span class="st">"https://github.com/pymc-devs/pymc-examples/raw/refs/heads/main/examples/data/cty.dat"</span>,</span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>radon_data <span class="op">=</span> (</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a> home_data</span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a> .rename(columns<span class="op">=</span><span class="bu">dict</span>(cntyfips<span class="op">=</span><span class="st">"ctfips"</span>))</span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a> .merge(</span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a> (</span>
<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a> county_data</span>
<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a> .drop_duplicates([<span class="st">'stfips'</span>, <span class="st">'ctfips'</span>, <span class="st">'st'</span>, <span class="st">'cty'</span>, <span class="st">'Uppm'</span>])</span>
<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a> .set_index([<span class="st">"ctfips"</span>, <span class="st">"stfips"</span>])</span>
<span id="cb7-22"><a href="#cb7-22" aria-hidden="true" tabindex="-1"></a> ),</span>
<span id="cb7-23"><a href="#cb7-23" aria-hidden="true" tabindex="-1"></a> right_index<span class="op">=</span><span class="va">True</span>,</span>
<span id="cb7-24"><a href="#cb7-24" aria-hidden="true" tabindex="-1"></a> left_on<span class="op">=</span>[<span class="st">"ctfips"</span>, <span class="st">"stfips"</span>],</span>
<span id="cb7-25"><a href="#cb7-25" aria-hidden="true" tabindex="-1"></a> )</span>
<span id="cb7-26"><a href="#cb7-26" aria-hidden="true" tabindex="-1"></a> .assign(log_radon<span class="op">=</span><span class="kw">lambda</span> x: np.log(np.clip(x.activity, <span class="fl">0.1</span>, np.inf)))</span>
<span id="cb7-27"><a href="#cb7-27" aria-hidden="true" tabindex="-1"></a> .assign(log_uranium<span class="op">=</span><span class="kw">lambda</span> x: np.log(np.clip(x[<span class="st">"Uppm"</span>], <span class="fl">0.1</span>, np.inf)))</span>
<span id="cb7-28"><a href="#cb7-28" aria-hidden="true" tabindex="-1"></a> .query(<span class="st">"state == 'MN'"</span>)</span>
<span id="cb7-29"><a href="#cb7-29" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>And also use the partially pooled model from the case-study:</p>
<div id="ce581edd" class="cell" data-execution_count="5">
<div class="sourceCode cell-code" 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>model_code <span class="op">=</span> <span class="st">"""</span></span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="st">data {</span></span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a><span class="st"> int<lower=1> N; // observations</span></span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a><span class="st"> int<lower=1> J; // counties</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a><span class="st"> array[N] int<lower=1, upper=J> county;</span></span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a><span class="st"> vector[N] x;</span></span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a><span class="st"> vector[N] y;</span></span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a><span class="st">parameters {</span></span>
<span id="cb8-10"><a href="#cb8-10" aria-hidden="true" tabindex="-1"></a><span class="st"> real mu_alpha;</span></span>
<span id="cb8-11"><a href="#cb8-11" aria-hidden="true" tabindex="-1"></a><span class="st"> real<lower=0> sigma_alpha;</span></span>
<span id="cb8-12"><a href="#cb8-12" aria-hidden="true" tabindex="-1"></a><span class="st"> vector<offset=mu_alpha, multiplier=sigma_alpha>[J] alpha; // non-centered parameterization</span></span>
<span id="cb8-13"><a href="#cb8-13" aria-hidden="true" tabindex="-1"></a><span class="st"> real beta;</span></span>
<span id="cb8-14"><a href="#cb8-14" aria-hidden="true" tabindex="-1"></a><span class="st"> real<lower=0> sigma;</span></span>
<span id="cb8-15"><a href="#cb8-15" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb8-16"><a href="#cb8-16" aria-hidden="true" tabindex="-1"></a><span class="st">model {</span></span>
<span id="cb8-17"><a href="#cb8-17" aria-hidden="true" tabindex="-1"></a><span class="st"> y ~ normal(alpha[county] + beta * x, sigma);</span></span>
<span id="cb8-18"><a href="#cb8-18" aria-hidden="true" tabindex="-1"></a><span class="st"> alpha ~ normal(mu_alpha, sigma_alpha); // partial-pooling</span></span>
<span id="cb8-19"><a href="#cb8-19" aria-hidden="true" tabindex="-1"></a><span class="st"> beta ~ normal(0, 10);</span></span>
<span id="cb8-20"><a href="#cb8-20" aria-hidden="true" tabindex="-1"></a><span class="st"> sigma ~ normal(0, 10);</span></span>
<span id="cb8-21"><a href="#cb8-21" aria-hidden="true" tabindex="-1"></a><span class="st"> mu_alpha ~ normal(0, 10);</span></span>
<span id="cb8-22"><a href="#cb8-22" aria-hidden="true" tabindex="-1"></a><span class="st"> sigma_alpha ~ normal(0, 10);</span></span>
<span id="cb8-23"><a href="#cb8-23" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb8-24"><a href="#cb8-24" aria-hidden="true" tabindex="-1"></a><span class="st">generated quantities {</span></span>
<span id="cb8-25"><a href="#cb8-25" aria-hidden="true" tabindex="-1"></a><span class="st"> array[N] real y_rep = normal_rng(alpha[county] + beta * x, sigma);</span></span>
<span id="cb8-26"><a href="#cb8-26" aria-hidden="true" tabindex="-1"></a><span class="st">}</span></span>
<span id="cb8-27"><a href="#cb8-27" aria-hidden="true" tabindex="-1"></a><span class="st">"""</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>We collect the dataset in the format that the stan model requires, and specify the dimensions of each of the non-scalar variables in the model:</p>
<div id="9a29bf02" class="cell" data-execution_count="6">
<div class="sourceCode cell-code" id="cb9"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>county_idx, counties <span class="op">=</span> pd.factorize(radon_data[<span class="st">"county"</span>], use_na_sentinel<span class="op">=</span><span class="va">False</span>)</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>observations <span class="op">=</span> radon_data.index</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>coords <span class="op">=</span> {</span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a> <span class="st">"county"</span>: counties,</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a> <span class="st">"observation"</span>: observations,</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a>dims <span class="op">=</span> {</span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a> <span class="st">"alpha"</span>: [<span class="st">"county"</span>],</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a> <span class="st">"y_rep"</span>: [<span class="st">"observation"</span>],</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a>data <span class="op">=</span> {</span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a> <span class="st">"N"</span>: <span class="bu">len</span>(observations),</span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a> <span class="st">"J"</span>: <span class="bu">len</span>(counties),</span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a> <span class="co"># Stan uses 1-based indexing!</span></span>
<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a> <span class="st">"county"</span>: county_idx <span class="op">+</span> <span class="dv">1</span>,</span>
<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a> <span class="st">"x"</span>: radon_data.log_uranium.values,</span>
<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a> <span class="st">"y"</span>: radon_data.log_radon.values,</span>
<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a>}</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Then, we compile the model and provide the dimensions, coordinates and the dataset we just defined:</p>
<div id="fe0286f3" class="cell" data-execution_count="7">
<div class="sourceCode cell-code" id="cb10"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>compiled_model <span class="op">=</span> (</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a> nutpie.compile_stan_model(code<span class="op">=</span>model_code)</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a> .with_data(<span class="op">**</span>data)</span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a> .with_dims(<span class="op">**</span>dims)</span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a> .with_coords(<span class="op">**</span>coords)</span>
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<div id="7a704cbf" class="cell" data-execution_count="8">
<div class="sourceCode cell-code" id="cb11"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="op">%%</span>time</span>
<span id="cb11-2"><a href="#cb11-2" aria-hidden="true" tabindex="-1"></a>trace <span class="op">=</span> nutpie.sample(compiled_model, seed<span class="op">=</span><span class="dv">0</span>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
<style>
:root {
--column-width-1: 40%; /* Progress column width */
--column-width-2: 15%; /* Chain column width */
--column-width-3: 15%; /* Divergences column width */
--column-width-4: 15%; /* Step Size column width */
--column-width-5: 15%; /* Gradients/Draw column width */
}
.nutpie {
max-width: 800px;
margin: 10px auto;
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
//color: #333;
//background-color: #fff;
padding: 10px;
box-shadow: 0 4px 6px rgba(0,0,0,0.1);
border-radius: 8px;
font-size: 14px; /* Smaller font size for a more compact look */
}
.nutpie table {
width: 100%;
border-collapse: collapse; /* Remove any extra space between borders */
}
.nutpie th, .nutpie td {
padding: 8px 10px; /* Reduce padding to make table more compact */
text-align: left;
border-bottom: 1px solid #888;
}
.nutpie th {
//background-color: #f0f0f0;
}
.nutpie th:nth-child(1) { width: var(--column-width-1); }
.nutpie th:nth-child(2) { width: var(--column-width-2); }
.nutpie th:nth-child(3) { width: var(--column-width-3); }
.nutpie th:nth-child(4) { width: var(--column-width-4); }
.nutpie th:nth-child(5) { width: var(--column-width-5); }
.nutpie progress {
width: 100%;
height: 15px; /* Smaller progress bars */
border-radius: 5px;
}
progress::-webkit-progress-bar {
background-color: #eee;
border-radius: 5px;
}
progress::-webkit-progress-value {
background-color: #5cb85c;
border-radius: 5px;
}
progress::-moz-progress-bar {
background-color: #5cb85c;
border-radius: 5px;
}
.nutpie .progress-cell {
width: 100%;
}
.nutpie p strong { font-size: 16px; font-weight: bold; }
@media (prefers-color-scheme: dark) {
.nutpie {
//color: #ddd;
//background-color: #1e1e1e;
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color: #ccc;
}
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}
.nutpie progress::-moz-progress-bar {
background-color: #3178c6;
}
}
</style>
</div>
<div class="cell-output cell-output-display">
<div class="nutpie">
<p><strong>Sampler Progress</strong></p>
<p>Total Chains: <span id="total-chains">6</span></p>
<p>Active Chains: <span id="active-chains">0</span></p>
<p>
Finished Chains:
<span id="active-chains">6</span>
</p>
<p>Sampling for now</p>
<p>
Estimated Time to Completion:
<span id="eta">now</span>
</p>
<progress id="total-progress-bar" max="8400" value="8400">
</progress>
<table>
<thead>
<tr>
<th>Progress</th>
<th>Draws</th>
<th>Divergences</th>
<th>Step Size</th>
<th>Gradients/Draw</th>
</tr>
</thead>
<tbody id="chain-details">
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>0.39</td>
<td>31</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>0.47</td>
<td>7</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>0.45</td>
<td>7</td>
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<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>0.46</td>
<td>7</td>
</tr>
<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
</progress>
</td>
<td>1400</td>
<td>0</td>
<td>0.45</td>
<td>7</td>
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<tr>
<td class="progress-cell">
<progress max="1400" value="1400">
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<td>1400</td>
<td>0</td>
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<td>7</td>
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</div>
<div class="cell-output cell-output-stdout">
<pre><code>CPU times: user 2.27 s, sys: 39.2 ms, total: 2.31 s
Wall time: 547 ms</code></pre>
</div>
</div>
<p>As some basic convergance checking we verify that all Rhat values are smaller than 1.02, all parameters have at least 500 effective draws and that we have no divergences:</p>
<div id="013fe62f" class="cell" data-execution_count="9">
<div class="sourceCode cell-code" id="cb13"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="cf">assert</span> trace.sample_stats.diverging.<span class="bu">sum</span>() <span class="op">==</span> <span class="dv">0</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a><span class="cf">assert</span> az.ess(trace).<span class="bu">min</span>().<span class="bu">min</span>() <span class="op">></span> <span class="dv">500</span></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="cf">assert</span> az.rhat(trace).<span class="bu">max</span>().<span class="bu">max</span>() <span class="op">></span> <span class="fl">1.02</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
</div>
<p>Thanks to the coordinates and dimensions we specified, the resulting trace will now contain labeled data, so that plots based on it have properly set-up labels:</p>
<div id="34452909" class="cell" data-execution_count="10">
<div class="sourceCode cell-code" id="cb14"><pre class="sourceCode python code-with-copy"><code class="sourceCode python"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> arviz <span class="im">as</span> az</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> seaborn <span class="im">as</span> sns</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a><span class="im">import</span> xarray <span class="im">as</span> xr</span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a>sns.catplot(</span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a> data<span class="op">=</span>trace.posterior.alpha.to_dataframe().reset_index(),</span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a> y<span class="op">=</span><span class="st">"county"</span>,</span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a> x<span class="op">=</span><span class="st">"alpha"</span>,</span>
<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a> kind<span class="op">=</span><span class="st">"boxen"</span>,</span>
<span id="cb14-10"><a href="#cb14-10" aria-hidden="true" tabindex="-1"></a> height<span class="op">=</span><span class="dv">13</span>,</span>
<span id="cb14-11"><a href="#cb14-11" aria-hidden="true" tabindex="-1"></a> aspect<span class="op">=</span><span class="dv">1</span><span class="op">/</span><span class="fl">2.5</span>,</span>
<span id="cb14-12"><a href="#cb14-12" aria-hidden="true" tabindex="-1"></a> showfliers<span class="op">=</span><span class="va">False</span>,</span>
<span id="cb14-13"><a href="#cb14-13" aria-hidden="true" tabindex="-1"></a>)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
<div class="cell-output cell-output-display">
<div>
<figure class="figure">
<p><img src="stan-usage_files/figure-html/cell-11-output-1.png" class="img-fluid figure-img"></p>
</figure>
</div>
</div>
</div>
</section>
</section>
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