Editing Markov chain Monte Carlo (section)

=== Gelman-Rubin Diagnostics ===

The [[Gelman-Rubin statistic]], also known as the '''potential scale reduction factor (PSRF)''', evaluates MCMC convergence by sampling multiple independent Markov chains and comparing within-chain and between-chain variances.<ref name="Gelman and Rubin, 1992">{{cite journal |last1=Gelman |first1=A. |last2=Rubin |first2=D.B. |date=1992 |title=Inference from iterative simulation using multiple sequences (with discussion) |url=http://www.stat.duke.edu/~scs/Courses/Stat376/Papers/ConvergeDiagnostics/GelmanRubinStatSci1992.pdf |journal=Statistical Science |volume=7 |issue=4 |pages=457–511 |bibcode=1992StaSc...7..457G |doi=10.1214/ss/1177011136 |doi-access=free}}</ref> If all chains have converged to the same stationary distribution, the between-chain and within-chain variances should be similar, and thus the PSRF must approach 1. In practice, a value of <math>< 1.1</math> is often taken as evidence of convergence. Higher values suggest that the chains are still exploring different parts of the target distribution.