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Estimating interactions in binary lattice data with nearest-neighbor property. (English) Zbl 0668.62059
The estimation problem for the interaction parameter $$U\in R^ 3$$ of a two-state Markov stationary Gibbs random field on $$({\mathbb{Z}}^+)^ 2$$ is considered. Let $$x_{D(m,n)}$$ be an observation of the field on a rectangular domain D(m,n) of size $$m\times n$$, and put $$\hat U_{m,n}$$ for the empirical minimum estimator for U from theorem 3.12 of the well- known book of D. Ruelle [Thermodynamic formalism. The mathematical structures of classical equilibrium. Statistical mechanics. (1978; Zbl 0401.28016)].
Theorem: $$\hat U_{m,n}\to U$$ almost sure for m,n$$\to \infty$$. An approximate calculation method for the values of $$\hat U_{m,n}$$ through $$x_{D(m,n)}$$, and an example are given.
Reviewer: E.I.Trofimov

##### MSC:
 62M05 Markov processes: estimation; hidden Markov models 62M99 Inference from stochastic processes 82B30 Statistical thermodynamics 80A10 Classical and relativistic thermodynamics
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##### References:
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