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Inference for general Ising models

Published online by Cambridge University Press:  14 July 2016

David K. Pickard
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Abstract

In previous papers (1976), (1977a), (1979) limit theorems were obtained for the classical Ising model, and these provided the basis for asymptotic inference. The present paper extends these results to more general Ising models.

In two and more dimensions, likelihood inference for the thermodynamic parameters (i.e. the interaction energies) is effectively impossible. The problem is that the error in locating critical and/or confidence regions is as large as their diameters. To remedy this requires more accurate characterizations of the partition functions, but these seem unlikely to be forthcoming. Besag's coding estimators for these parameters are inverse hyperbolic tangents of the roots of simultaneous polynomial equations and hence avoid such location errors. However, little is yet known about their sampling characteristics. Finally, likelihood inference for lattice averages (an alternative parametrization) is straightforward from the limit theorems.

Keywords

ISING MODELSGIBBS ENSEMBLESAUTO-LOGISTIC MODELSNEAREST-NEIGHBOR MODELSMARKOV FIELDSLATTICE MODELSCENTRAL LIMIT THEOREMASYMPTOTIC INFERENCECODING ESTIMATORS
Type
Part 6 — Stochastic Processes
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 345 - 357
Copyright
Copyright © 1982 Applied Probability Trust 

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