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

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

2010-11-29

arxiv.org/abs/1011.6217v1

Statistical Science 2010, Vol. 25, No. 2, 172-190

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/10-STS327 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

10.1214/10-STS327

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.

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