er:2011">2011</a>)</span> for more detail on using FFT for autocorrelation calculations. The autocorrelation estimates <span class="math inline">\(\hat{\rho}_{t,m}\)</span> at lag <span class="math inline">\(t\)</span> from multiple chains <span class="math inline">\(m \in (1,\ldots,M)\)</span> are combined with within-sample variance estimate <span class="math inline">\(W\)</span> and multi-chain variance estimate <span class="math inline">\(\widehat{\mbox{var}}^{+}\)</span> introduced in the previous sect