Motivated by applications in texture synthesis, we propose a model selection procedure for Markov random fields based on penalized pseudolikelihood. The procedure is shown to be consistent for choosing the true model, even for Gibbs random fields with phase transitions. As a by-product, rates for the restricted mean-square error and moderate deviation probabilities are derived for the maximum pseudolikelihood estimator. Some simulation results are presented for the selection procedure.
"A consistent model selection procedure for Markov random fields based on penalized pseudolikelihood." Ann. Appl. Probab. 6 (2) 423 - 443, May 1996. https://doi.org/10.1214/aoap/1034968138