On the use of a local $\hat R$ to improve MCMC convergence diagnostic - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Bayesian Analysis Year : 2023

On the use of a local $\hat R$ to improve MCMC convergence diagnostic

Abstract

Diagnosing 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 $\hat R$, 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 $\hat R$ behaviour by proposing a localized version that focuses on 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 $\hat R_\infty$, 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 $\hat R$ versions.
Fichier principal
Vignette du fichier
BA_draft_Rhat.pdf (1.19 Mo) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03600407 , version 1 (07-03-2022)
hal-03600407 , version 2 (07-03-2023)

Licence

Attribution

Identifiers

Cite

Théo Moins, Julyan Arbel, Anne Dutfoy, Stéphane Girard. On the use of a local $\hat R$ to improve MCMC convergence diagnostic. Bayesian Analysis, 2023, ⟨10.1214/23-BA1399⟩. ⟨hal-03600407v2⟩
142 View
206 Download

Altmetric

Share

Gmail Facebook X LinkedIn More