ta <span class="math inline">\((x, y).\)</span></p>
<p>This integral may be calculated with Monte Carlo methods as usual, <span class="math display">\[
p(\tilde{y} \mid \tilde{x}, x, y)
\approx
\frac{1}{M} \sum_{m = 1}^M p(\tilde{y} \mid \tilde{x}, \theta^{(m)}),
\]</span> where the <span class="math inline">\(\theta^{(m)} \sim p(\theta \mid x, y)\)</span> are draws from the posterior given only the training data <span class="math inline">\((x, y).\)</span></p>
<p>To avoid underflow in calculations, it will