New models for markov random-fields

Authors

Noel A. Cressie, University of WollongongFollow
Subhash Lele

RIS ID

73453

Publication Details

Cressie, N. A. & Lele, S. (1992). New models for markov random-fields. Journal Of Applied Probability, 29 (4), 877-884.

Abstract

The Hammersley-Clifford theorem gives the form that the joint probability density (or mass) function of a Markov random field must take. Its exponent must be a sum of functions of variables, where each function in the summand involves only those variables whose sites form a clique. From a statistical modeling point of view, it is important to establish the converse result, namely, to give the conditional probability specifications that yield a Markov random field. Besag (1974) addressed this question by developing a one-parameter exponential family of conditional probability models. In this article, we develop new models for Markov random fields by establishing sufficient conditions for the conditional probability specifications to yield a Markov random field.