span class="math display">\[
\hat{\sigma}_n = \mathrm{sd}(\theta^{(1)}_n, \ldots, \theta^{(m)}_n).
\]</span></p>
<p>The previous section showed how to estimate <span class="math inline">\(N_{\mathrm{eff}}\)</span> for a parameter <span class="math inline">\(\theta_n\)</span> based on multiple chains of posterior draws.</p>
<p>The mean of the posterior draws of <span class="math inline">\(\theta_n\)</span> <span class="math display">\[
\hat{\theta}_n
= \mathrm{mean}(\theta^{(1)}_n, \ldots, \theta^{(m)}_n)
\]