n^{(m)}\)</span>, the same result is obtained by averaging linear predictions, <span class="math display">\[\begin{eqnarray*}
\hat{\tilde{y}}_n
&amp; = &amp; \mathbb{E}\left[
          \alpha + \beta \cdot \tilde{x}_n
          \mid \tilde{x}_n, x, y
       \right]
\\[4pt]
&amp; \approx &amp;
\frac{1}{M} \sum_{m = 1}^M
  \alpha^{(m)} + \beta^{(m)} \cdot \tilde{x}_n.
\end{eqnarray*}\]</span> This is possible because <span class="math display">\[
\tilde{y}_n^{(m)} \sim \textrm{normal}(\tilde{y}_n \mid \alpha^