 though <span class="math inline">\(p(y \mid \theta)\)</span> can’t be represented, there is no problem representing</p>
<p><span class="math display">\[
\begin{array}{rcl}
\log p(y \mid \theta)
&amp; = &amp; \log \prod_{n=1}^N p(y_n \mid \theta)
\\[4pt]
&amp; = &amp; \sum_{n = 1}^N \log p(y_n \mid \theta)
\end{array}
\]</span></p>
<p>This is why all of Stan’s probability functions operate on the log
scale.</p>
</div>
<div id="adding-on-the-log-scale" class="section level3">
<h3><span class="header-sect