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We consider the problem of estimating the interacting neighborhood of aMarkov Random Field model with finite support and homogeneous pairwiseinteractions based on relative positions of a two-dimensional lattice. Using aBayesian framework, we propose a Reversible Jump Monte Carlo Markov Chainalgorithm that jumps across subsets of a maximal range neighborhood, allowingus to perform model selection based on a marginal pseudoposterior distributionof models. To show the strength of our proposed methodology we perform asimulation study and apply it to a real dataset from a discrete texture imageanalysis.

Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors