Inference for Discrete Markov Fields: The Simplest Nontrivial Case
本文以经典伊辛模型为例，说明离散马尔可夫场在似然推断中面临归一化常数计算困难、相位转变和长程相互作用导致可识别性问题，适合关注空间统计或统计物理的学者判断是否阅读原文。
Abstract Abstract Markov fields provide a general context for describing the strength and structure of spatial interactions. The Gibbs—Markov equivalence theorem (Preston 1974) parameterizes Markov fields via their neighborhood structures, yielding exponential families in canonical form. Likelihood inference is, therefore, apparently straightforward. The requisite normalizing constants, however, are obstreperous. Even when asymptotic characterizations can be obtained, substantial location errors arise during implementation. Moreover, Markov fields can exhibit phase transitions and long-range interactions, thereby creating identifiability problems. These issues are illustrated in the simplest nontrivial case—the classical Ising model of ferromagnetism.