Fully Bayesian Binary Markov Random Field Models: Prior Specification and Posterior Simulation

We propose a flexible prior model for the parameters of binary Markov random fields (MRF), defined on rectangular lattices and with maximal cliques defined from a template maximal clique. The prior model allows higher‐order interactions to be included. We also define a reversible jump Markov chain Monte Carlo algorithm to sample from the associated posterior distribution. The number of possible parameters for a higher‐order MRF becomes high, even for small template maximal cliques. We define a flexible parametric form where the parameters have interpretation as potentials for clique configurations, and limit the effective number of parameters by assigning apriori discrete probabilities for events where groups of parameter values are equal. To cope with the computationally intractable normalising constant of MRFs, we adopt a previously defined approximation of binary MRFs. We demonstrate the flexibility of our prior formulation with simulated and real data examples.