Applications
of Bartolucci's theorem
Julian Besag
Ordinary and
hidden Markov random fields (MRF's) play an important
role in Environmental Statistics and in many other
areas. However, understanding of MRF-based formulations
is often hampered by the extreme difficulties in
theoretical analysis and effective simulation. This
project will clarify some of the issues and also promote
the use of conditional specifications.
In
principle, MRF's are ideally suited to Markov chain
Monte Carlo (MCMC) methods but, in practice,
componentwise samplers, such as the ordinary Gibbs
sampler, may lack adequate mobility around the sample
space. Potentially, the problem can be solved by block
updating but this is usually difficult to implement.
Very recently, Dr. Francesco Bartolucci (University of
Perugia, Italy) has devised a new recursion for MRF
marginalization and he and I will be investigating its
potential during the project. If time permits, other
features of MRF formulations will also be considered.
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