Approximate Bayes model selection procedures for Gibbs-Markov random fields
type: Item
instance of: scholarly article
title: Approximate Bayes model selection procedures for Gibbs-Markov random fields
zbMATH Open document ID: 0851.62067
DOI: 10.1016/0378-3758(95)00071-2
author: Lynne Seymour
author: Chuanshu Ji
published in: Journal of Statistical Planning and Inference
publication date: 1996-11-11T00:00:00Z
review text: Markov random fields (MRFs) were originally introduced as models in statistical mechanics during the early 1990s. This work is motivated by texture synthesis: For an image consisting of a single texture with no degradation, we seek to choose a model from a collection of MRFs which produces typical samples resembling real textures. Since the likelihood for MRFs may be written as an exponential family, we take an approach similar to that of \textit{G. Schwarz} [Ann. Stat. 6, 461-464 (1978; Zbl 0379.62005)] to derive approximate Bayesian information criteria (BIC) for choosing a ``best'' model. In Section 2 we give a brief introduction to random fields, a Bayesian formulation of the model selection problem, and our main results. Section 3 is devoted to the likelihood and Markov chain Monte Carlo likelihood, which are basic elements in our solution to the model selection problem. In Section 4, we present a small simulation study of our results. All technical proofs are kept in Section 5.
Mathematics Subject Classification ID: 62M40
Mathematics Subject Classification ID: 62F15
zbMATH DE Number: 906643
zbMATH Keywords: penalized maximum likelihood
zbMATH Keywords: Gibbs random field
zbMATH Keywords: Markov random fields
zbMATH Keywords: texture synthesis
zbMATH Keywords: exponential family
zbMATH Keywords: approximate Bayesian information criteria
zbMATH Keywords: model selection
zbMATH Keywords: Markov chain Monte Carlo likelihood
zbMATH Keywords: simulation study
describes a project that uses: spatial
MaRDI profile type: Publication
full work available at URL: 0378-3758(95)00071-2
OpenAlex ID: W2050990188
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description: scientific article; zbMATH DE number 906643