Title: Improving MCMC convergence diagnostic with a local version of R-hat
Authors: Theo Moins - Inria (France) [presenting]
Julyan Arbel - Inria (France)
Anne Dutfoy - EDF (France)
Stephane Girard - Inria (France)
Abstract: 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.