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The potential scale reduction factor compares variation within simulated chains to a variance estimate also incorporating differences between chains. In its classical form, $\hat{R}=\sqrt{\hat{V}/W}$, 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.^[ref]

The Stan Development Team is the collective author credited for Stan's statistical modeling manuals. The Stan Reference Manual by Stan Development Team documents the language and inference methods; the Stan User's Guide by Stan Development Team develops model construction and applied examples.

Its treatment of posterior analysis explains diagnostics such as effective sample size and split R-hat for Markov chain Monte Carlo. These assess features of finite sampled output and do not turn a finite run into a proof of exact convergence.^[ref]