Consistent estimation of the basic neighborhood of markov random fields

Imre Csiszár, Zsolt Talata

Research output: Contribution to journalArticle

33 Citations (Scopus)

Abstract

For Markov random fields on ℤ d 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.

Original languageEnglish
Pages (from-to)123-145
Number of pages23
JournalAnnals of Statistics
Volume34
Issue number1
DOIs
Publication statusPublished - Feb 1 2006

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Keywords

  • Gibbs measure
  • Information criterion
  • Markov random field
  • Model selection
  • Pseudo-likelihood
  • Typicality

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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