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1 results

  • New models for Markov random fields

  • Part of
  • Noel Cressie, Subhash Lele
  • Journal:
    Journal of Applied Probability / Volume 29 / Issue 4 / December 1992
    Published online by Cambridge University Press:
    14 July 2016, pp. 877-884
    Print publication:
    December 1992

  • 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.