Research Summary

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.