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February 2006 Consistent estimation of the basic neighborhood of Markov random fields
Imre Csiszár, Zsolt Talata
Ann. Statist. 34(1): 123-145 (February 2006). DOI: 10.1214/009053605000000912


For Markov random fields on ℤd with finite state space, we address the statistical estimation of the basic neighborhood, the smallest region that determines the conditional distribution at a site on the condition that the values at all other sites are given. A modification of the Bayesian Information Criterion, replacing likelihood by pseudo-likelihood, is proved to provide strongly consistent estimation from observing a realization of the field on increasing finite regions: the estimated basic neighborhood equals the true one eventually almost surely, not assuming any prior bound on the size of the latter. Stationarity of the Markov field is not required, and phase transition does not affect the results.


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Imre Csiszár. Zsolt Talata. "Consistent estimation of the basic neighborhood of Markov random fields." Ann. Statist. 34 (1) 123 - 145, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1102.62105
MathSciNet: MR2275237
Digital Object Identifier: 10.1214/009053605000000912

Primary: 60G60 , 62F12
Secondary: 62M40 , 82B20

Keywords: Gibbs measure , information criterion , Markov random field , Model selection , pseudo-likelihood , typicality

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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