The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 1 (2006), 123-145.
Consistent estimation of the basic neighborhood of Markov random fields
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.
Ann. Statist., Volume 34, Number 1 (2006), 123-145.
First available in Project Euclid: 2 May 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G60: Random fields 62F12: Asymptotic properties of estimators
Secondary: 62M40: Random fields; image analysis 82B20: Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Csiszár, Imre; Talata, Zsolt. Consistent estimation of the basic neighborhood of Markov random fields. Ann. Statist. 34 (2006), no. 1, 123--145. doi:10.1214/009053605000000912. https://projecteuclid.org/euclid.aos/1146576258