 \right)
\\[4pt]
&amp; = &amp; \frac{1}{M} \sum_{m = 1}^M \alpha^{(m)}
      + \frac{1}{M} \sum_{m = 1}^M (\beta^{(m)} \cdot \tilde{x}_n)
\\[4pt]
&amp; = &amp; \frac{1}{M} \sum_{m = 1}^M \alpha^{(m)}
      + \left( \frac{1}{M} \sum_{m = 1}^M \beta^{(m)}\right) \cdot \tilde{x}_n
\\[4pt]
&amp; = &amp; \hat{\alpha} + \hat{\beta} \cdot \tilde{x}_n.
\end{eqnarray*}\]</span></p>
<p>In Stan, only the first of the two steps (the important variance reduction step) can be coded in the object model. The linear predict