C Sherlock, P Fearnhead and GO Roberts
The random walk Metropolis: linking theory and practice through a case study
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 reparameterisation of the MMPP which leads to a highly efficient RWM within Gibbs algorithm in certain circumstances is also developed.
Keywords: Random walk Metropolis, Metropolis-Hastings, MCMC, adaptive MCMC, MMPP.