A Bayesian model for the dependence structure in binary Markov random fields.

Abstract

In this thesis a reversible jump Markov chain Monte Carlo (MCMC) method for simulation of the graph structure of a binary Markov random field (MRF) is presented. The reversible jump MCMC method allows for simulation of both the graph structure and the parameter values of the MRF. First a Bayesian model for the problem is described. The prior model used is a slightly altered version of the spike and slab prior used by Chen and Welling (2012). Next the algorithm for simulation is presented and the method is then tested for simulated datasets of different sized based on two example graphs. The algorithm is able to find models that give good fits to most of the datasets, but we see signs of the algorithm not converging properly.