Consistent estimation of the basic neighborhood of Markov random fields
针对有限状态空间上的马尔可夫随机场，提出一种修改的贝叶斯信息准则（用伪似然替代似然），证明在观测区域增大时能一致估计基本邻域，且无需假设邻域大小上界或场平稳性。
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.