Consistent estimation of the basic neighborhood of Markov random fields

• 成果类型: Article
• 署名作者: Csiszár, I; Talata, Z
• 署名单位: Hungarian Academy of Sciences; HUN-REN; HUN-REN Alfred Renyi Institute of Mathematics
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000912
• 发表日期: 2006
• 页码: 123-145
• 关键词: order; lattice; MODEL; mdl

摘要

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.