edictive-likelihood" class="section level4">
<h4 class="unnumbered" number="">Predictive likelihood</h4>
<p>Predictive likelihood for a new observation <span class="math inline">\(\tilde{y}\)</span> given the
complete parameter vector <span class="math inline">\(\theta\)</span> will be</p>
<p><span class="math display">\[
p(\tilde{y} \, | \, y)
=
\int_{\theta}
p(\tilde{y} \, | \, \theta)
\, p(\theta | y)
\, \mbox{d}\theta.
\]</span></p>
<p>The normal mixture example from the previous section, with <span cla