n calculating the potential-scale-reduction statistic
<span class="math inline">\(\hat{R}\)</span>, each chain is split into two halves. This provides an
additional means to detect non-stationarity in the individual chains.
If one chain involves gradually increasing values and one involves
gradually decreasing values, they have not mixed well, but they can
have <span class="math inline">\(\hat{R}\)</span> values near unity. In this case, splitting each chain
into two parts leads to <span class="math inline"