To investigate interactions between parasite species in a host a population
of field voles was studied longitudinally with presence or absence of six
different parasites measured repeatedly.
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).
Scaling of proposals for Metropolis algorithms is an important practical
problem in MCMC implementation. Criteria for scaling based on empirical
acceptance rates of algorithms have been found to work consistently well across
a broad range of problems. Essentially, proposal jump sizes are increased when
acceptance rates are high and decreased when rates are low. In recent years,
considerable theoretical support has been given for rules of this type which
work on the basis that acceptance rates around 0.234 should be preferred.
Scaling of proposals for Metropolis algorithms is an important practical
problem in MCMC implementation. Criteria for scaling based on empirical
acceptance rates of algorithms have been found to work consistently well across
a broad range of problems. Essentially, proposal jump sizes are increased when
acceptance rates are high and decreased when rates are low. In recent years,
considerable theoretical support has been given for rules of this type which
work on the basis that acceptance rates around 0.234 should be preferred.