Generalized Ising models and their applications

The Ising model has become more prominent in spatial statistics since its applications in image analysis, as pioneered by Besag. This paper describes three multilevel generalizations of the Ising model, including the general spin Ising model. We compare and contrast these three generalizations. In all three cases, the normalizing constant is intractable but, using the developments made by physicists, we give adequate approximations for the general spin model, together with complete expressions for the binary Ising model. We show that these approximations allow inference for the general spin model. An application to texture analysis is also given.