+t)}\)</span> have the same marginal distribution in an MCMC setting, multiplying the two difference terms and reducing yields</p>
<p><span class="math display">\[
\rho_t
= \frac{1}{\sigma^2}
\, \int_{\Theta}
      \theta^{(n)} \, \theta^{(n+t)} \, p(\theta)
   \, d\theta - \frac{\mu^2}{\sigma^2}.
\]</span></p>
<p>The effective sample size of <span class="math inline">\(N\)</span> samples generated by a process with autocorrelations <span class="math inline">\(\rho_t\)</span> is defined by <span class="math