= Markov chain Monte Carlo convergence diagnostics
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Several chains from dispersed initial states, trace plots, <autocorrelation>, effective sample sizes, and the rank-normalized split potential scale reduction factor $\widehat R$ assess mixing and disagreement between chains. An $\widehat R$ close to one is useful evidence but cannot prove convergence or prove <posterior propriety>. Comparing chains that explore different modes is especially important; monitor each scientifically important observable and its Monte Carlo uncertainty. A long apparent plateau can also occur when an improper-target sampler is drifting toward a boundary.
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