Parallel hierarchical sampling: a practical multiple-chains sampler for Bayesian model selection

TL;DR

This paper presents the parallel hierarchical sampler (PHS), a multi-chain MCMC method for Bayesian model selection, demonstrating its convergence and practical advantages over existing algorithms like parallel tempering and Metropolis-Hastings.

Contribution

The paper introduces PHS, a new multi-chain MCMC algorithm with proven convergence, and compares its effectiveness to existing methods in various Bayesian model selection tasks.

Findings

PHS converges reliably in Bayesian model selection.

PHS outperforms parallel tempering and Metropolis-Hastings in practical problems.

PHS provides efficient inference for complex Bayesian models.

Abstract

This paper introduces the parallel hierarchical sampler (PHS), a Markov chain Monte Carlo algorithm using several chains simultaneously. The connections between PHS and the parallel tempering (PT) algorithm are illustrated, convergence of PHS joint transition kernel is proved and and its practical advantages are emphasized. We illustrate the inferences obtained using PHS, parallel tempering and the Metropolis-Hastings algorithm for three Bayesian model selection problems, namely Gaussian clustering, the selection of covariates for a linear regression model and the selection of the structure of a treed survival model.