Inference for Discrete Markov Fields: The Simplest Nontrivial Case
- 1 March 1987
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 82 (397) , 90
- https://doi.org/10.2307/2289128
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.Keywords
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