The Random Walk Metropolis: Linking Theory and Practice Through a Case Study

TL;DR

This paper reviews key theoretical and practical aspects of the Random Walk Metropolis algorithm, illustrating their implications through a case study on Markov modulated Poisson processes and proposing a reparameterization for improved efficiency.

Contribution

It synthesizes existing and new results on RWM, demonstrating their practical impact and introducing a reparameterization to enhance algorithm efficiency in specific scenarios.

Findings

Reparameterization improves RWM efficiency for MMPP

Theoretical insights inform practical algorithm design

Case study validates new approaches

Abstract

The random walk Metropolis (RWM) is one of the most common Markov chain Monte Carlo algorithms in practical use today. Its theoretical properties have been extensively explored for certain classes of target, and a number of results with important practical implications have been derived. This article draws together a selection of new and existing key results and concepts and describes their implications. The impact of each new idea on algorithm efficiency is demonstrated for the practical example of the Markov modulated Poisson process (MMPP). A reparameterization of the MMPP which leads to a highly efficient RWM-within-Gibbs algorithm in certain circumstances is also presented.