es \prod_{n=1}^N \textsf{Bernoulli}(y_n \mid \phi) \\
 &amp;=
   \textsf{beta}\left(\phi \,\middle|\, 0.5 + \sum_{n=1}^N y_n, 0.5 + N - \sum_{n=1}^N y_n\right).
\end{align*}\]</span></p>
<p>If <span class="math inline">\(N = 9\)</span> and each <span class="math inline">\(y_n = 1\)</span>, the posterior is
<span class="math inline">\(\textsf{beta}(\phi \mid 9.5,0,5)\)</span>. This posterior is unbounded as <span class="math inline">\(\phi \rightarrow 1\)</span>. Nevertheless, the posterior is proper, and al