= \frac{1}{M} \, \sum_{m=1}^M \bar{\theta}_m^{(\bullet)}.
\]</span></p>
<p>The <em>within-chain variance</em> is averaged over the chains,</p>
<p><span class="math display">\[
W = \frac{1}{M} \, \sum_{m=1}^M s_m^2,
\]</span></p>
<p>where</p>
<p><span class="math display">\[
s_m^2
=
\frac{1}{N-1}
\, \sum_{n=1}^N (\theta^{(n)}_m - \bar{\theta}^{(\bullet)}_m)^2.
\]</span></p>
<p>The <em>variance estimator</em> is a mixture of the within-chain and
cross-chain sample variances,</p>
<p><span class="math display">