Loading...
Consistent estimation of the basic neighborhood of Markov random fields
Csiszar, Imre Talata, Zsolt
Csiszar, Imre
Talata, Zsolt
Citations
Altmetric:
Abstract
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.
Description
This is the published version, also available here: http://dx.doi.org/10.1214/009053605000000912.
Date
2006-10-05
Journal Title
Journal ISSN
Volume Title
Publisher
Institute of Mathematical Statistics
Collections
Research Projects
Organizational Units
Journal Issue
Keywords
Markov random field, pseudo-likelihood, Gibbs measure, model selection, information criterion, typicality
Citation
Csiszár, Imre; Talata, Zsolt. Consistent estimation of the basic neighborhood of Markov random fields. Ann. Statist. 34 (2006), no. 1, 123--145. http://dx.doi.org/10.1214/009053605000000912.