Penalised t-walk MCMC

TL;DR

This paper introduces penalised t-walk MCMC, an extension of the t-walk algorithm designed to better handle multimodal distributions in complex statistical models, aiming for improved mixing and convergence.

Contribution

The paper proposes novel penalised t-walk extensions for multimodal MCMC sampling, along with a post-processing technique based on pseudo-marginal theory for isolated sample combination.

Findings

Enhanced mixing in multimodal distributions

Reduced computational cost compared to existing methods

Effective post-processing for complex scenarios

Abstract

Handling multimodality that commonly arises from complicated statistical models remains a challenge. Current Markov chain Monte Carlo (MCMC) methodology tackling this subject is based on an ensemble of chains targeting a product of power-tempered distributions. Despite the theoretical validity of such methods, practical implementations typically suffer from bad mixing and slow convergence due to the high-computation cost involved. In this work we study novel extensions of the t-walk algorithm, an existing MCMC method that is inexpensive and invariant to affine transformations of the state space, for dealing with multimodal distributions. We acknowledge that the effectiveness of the new method will be problem dependent and might struggle in complex scenarios; for such cases we propose a post-processing technique based on pseudo-marginal theory for combining isolated samples.