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

• URL: http://arxiv.org/abs/2204.05933v4
• Date: Tue, 30 Apr 2024 15:51:59 GMT
• Title: Sparse Interaction Neighborhood Selection for Markov Random Fields via Reversible Jump and Pseudoposteriors
• Authors: Victor Freguglia, Nancy Lopes Garcia,
• Abstract summary: We consider the problem of estimating the interacting neighborhood of a Markov Random Field model with finite support and homogeneous pairwise interactions. We propose a Reversible Jump Monte Carlo Markov Chain algorithm that jumps across subsets of a maximal range neighborhood.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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