or a chain with joint
probability function <span class="math inline">\(p(\theta)\)</span> with mean <span class="math inline">\(\mu\)</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-