an class="math inline">\(\textsf{beta}(\phi \mid 0.5,0.5)\)</span>, which can arise if seemingly weak beta
priors are used for groups that have no data. This density is
unbounded as <span class="math inline">\(\phi \rightarrow 0\)</span> and <span class="math inline">\(\phi \rightarrow 1\)</span>. Similarly,
a Bernoulli likelihood model coupled with a “weak” beta prior, leads
to a posterior
<span class="math display">\[\begin{align*}
p(\phi \mid y)
 &amp;\propto 
   \textsf{beta}(\phi \mid 0.5,0.5) \tim