  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.
