= Potential scale reduction factor
{title2=$\widehat R$}
= R-hat
{c}
{synonym}
The <potential scale reduction factor> compares variation within simulated chains to a variance estimate also incorporating differences between chains. In its classical form, $\widehat R=\sqrt{\widehat V/W}$, where $W$ is the average within-chain <sample variance>. Values appreciably above one indicate disagreement; values close to one do not prove convergence. Splitting chains helps expose changes over time, and modern rank-based variants improve robustness.<Stan Reference Manual by Stan Development Team>[Posterior Analysis, “Potential scale reduction”, “Split R-hat for detecting non-stationarity”, and “Rank normalization helps when there are heavy tails”]{ref}
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