mu\)</span> and variance <span class="math inline">\(\sigma^2\)</span> is defined to be</p>
<p><span class="math display">\[
\rho_t
=
\frac{1}{\sigma^2} \, \int_{\Theta} (\theta^{(n)} - \mu)
(\theta^{(n+t)} - \mu) \, p(\theta) \, d\theta.
\]</span></p>
<p>This is the correlation between the two chains offset by <span class="math inline">\(t\)</span> positions (i.e., a lag in time-series terminology). Because we know <span class="math inline">\(\theta^{(n)}\)</span> and <span class="math inline">\(\theta^{(n