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

TL;DR

This paper introduces a Bayesian Reversible Jump MCMC method for selecting the interaction neighborhood in 2D Markov Random Fields, demonstrated through simulations and texture image analysis.

Contribution

It develops a novel Bayesian model selection approach using Reversible Jump MCMC for neighborhood estimation in Markov Random Fields.

Findings

Effective neighborhood selection demonstrated in simulations

Successful application to texture image analysis

Bayesian pseudoposterior provides reliable model inference

Abstract

We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions based on relative positions of a two-dimensional lattice. Using a Bayesian framework, we propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood, allowing us to perform model selection based on a marginal pseudoposterior distribution of models. To show the strength of our proposed methodology we perform a simulation study and apply it to a real dataset from a discrete texture image analysis.