Prior specification for binary Markov mesh models

Abstract: We propose prior distributions for all parts of the specification of a Markov mesh model. In the formulation we define priors for the sequential neighborhood, for the parametric form of the conditional distributions and for the parameter values. By simulating from the resulting posterior distribution when conditioning on an observed scene, we thereby obtain an automatic model selection procedure for Markov mesh models. To sample from such a posterior distribution, we construct a reversible jump Markov chain Monte Carlo algorithm (RJMCMC). We demonstrate the usefulness of our prior formulation and the limitations of our RJMCMC algorithm in two examples.