 \sum_{m = 1}^M \tilde{y}_n^{(m)}
\end{eqnarray*}\]</span> where <span class="math inline">\(\tilde{y}_n^{(m)}\)</span> is drawn from the data model <span class="math display">\[
\tilde{y}_n^{(m)}
\sim p(\tilde{y}_n \mid \tilde{x}_n, \alpha^{(m)}, \beta^{(m)}),
\]</span> for parameters <span class="math inline">\(\alpha^{(m)}\)</span> and <span class="math inline">\(\beta^{(m)}\)</span> drawn from the posterior, <span class="math display">\[
(\alpha^{(m)}, \beta^{(m)}) \sim p(\alpha, \beta \mid x, y).
\]</s