{(m)} +
\beta^{(m)} \cdot \tilde{x}_n, \sigma^{(m)}),
\]</span> and the normal distribution has symmetric error so that the expectation of <span class="math inline">\(\tilde{y}_n^{(m)}\)</span> is the same as <span class="math inline">\(\alpha^{(m)} + \beta^{(m)} \cdot
\tilde{x}_n\)</span>. Replacing the sampled quantity <span class="math inline">\(\tilde{y}_n^{(m)}\)</span> with its expectation is a general variance reduction technique for Monte Carlo estimates known as <em>Rao-Blackwellization</em> <span 