Improving MCMC convergence diagnostic with a local version of R-hat

Théo Moins (1) , Julyan Arbel (1) , Anne Dutfoy (2) , Stéphane Girard (1)

1 STATIFY - Modèles statistiques bayésiens et des valeurs extrêmes pour données structurées et de grande dimension
2 EDF R&D PERICLES - PERformance et prévention des Risques Industriels du parC par la simuLation et les EtudeS

Diagnosing the convergence of Markov chain Monte Carlo is crucial and remains an essentially unsolved problem. Among the most popular methods, the potential scale reduction factor, commonly named R-hat, is an indicator that monitors the convergence of output chains to a target distribution, based on a comparison of the between- and within-variances. Several improvements have been suggested since its introduction in the 90s. Here, we aim at better understanding the R-hat behavior by proposing a localized version that focuses on the quantiles of the target distribution. This new version relies on key theoretical properties of the associated population value. It naturally leads to proposing a new indicator R-hat-infinity, which is shown to allow both for localizing the Markov chain Monte Carlo convergence in different quantiles of the target distribution, and at the same time, for handling some convergence issues not detected by other R-hat versions.

Domaines: Statistiques [math.ST]

Théo Moins, Julyan Arbel, Anne Dutfoy, Stéphane Girard. Improving MCMC convergence diagnostic with a local version of R-hat. CMStatistics 2022 - 15th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2022, London, United Kingdom. ⟨hal-03910658⟩