Prior specification for binary Markov mesh models

TL;DR

This paper introduces a comprehensive prior specification for binary Markov mesh models and develops an RJMCMC algorithm for automatic model selection based on posterior sampling.

Contribution

It proposes a new prior framework for all components of binary Markov mesh models and implements an RJMCMC method for automatic model selection.

Findings

Effective prior formulation demonstrated in examples

RJMCMC algorithm enables automatic model selection

Limitations of the method identified in practical applications

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.