A Mixture-Based Approach to Regional Adaptation for MCMC

TL;DR

This paper introduces RAPTOR, a mixture-based regional adaptation method for MCMC that uses online EM to efficiently partition the sample space, improving adaptive sampling in complex distributions.

Contribution

It proposes a novel mixture model approach with online EM for regional adaptation in MCMC, enabling efficient online implementation.

Findings

Effective on simulated data

Successful application to real data

Reduces computational load during adaptation

Abstract

Recent advances in adaptive Markov chain Monte Carlo (AMCMC) include the need for regional adaptation in situations when the optimal transition kernel is different across different regions of the sample space. Motivated by these findings, we propose a mixture-based approach to determine the partition needed for regional AMCMC. The mixture model is fitted using an online EM algorithm (see Andrieu and Moulines, 2006) which allows us to bypass simultaneously the heavy computational load and to implement the regional adaptive algorithm with online recursion (RAPTOR). The method is tried on simulated as well as real data examples.