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<p>and have no distribution statement for <code>theta</code> in the <code>model</code> block, then you are implicitly assigning an improper uniform prior on <span class="math inline">\((-\infty,\infty)\)</span> to <code>theta</code>.</p>
<p>BUGS models are always proper (being constructed as a product of proper marginal and conditional densities). Stan models can be improper. Here is the simplest improper Stan model:</p>
<div class="sourceCode" id="cb19"><pre class="sourceCode stan c