 display">\[
N_{\mathrm{eff}}
\ = \
\frac{N}{\sum_{t = -\infty}^{\infty} \rho_t}
\ = \
\frac{N}{1 + 2 \sum_{t = 1}^{\infty} \rho_t}.
\]</span></p>
<p>Effective sample size <span class="math inline">\(N_{\mathrm{eff}}\)</span> can be larger than <span class="math inline">\(N\)</span> in case of antithetic Markov chains, which have negative autocorrelations on odd lags. The no-U-turn sampling (NUTS) algorithm used in Stan can produce <span class="math inline">\(N_{\mathrm{eff}}&gt;N\)</span> for parameters wh