Development Of Markov Random Field Models Based On Exponential Family Conditional Distributions

Constructing statistical models through the specification of conditional distributions is being recognized as an appealing approach to a multivariate data analysis. A useful class of such models may be formulated by assuming that the conditional distributions are specified as exponential families. The class of exponential family conditional (EFC) models is expected to provide a general model framework that may be applied to a wide variety of situations that may contain complex dependence structures. The overall objective of this study is to develop and refine the general methodology for EFC models. Among a number of EFC models that have been studied so far, the Gaussian conditionals family has attracted a major interest, both theoretically and practically, and has been applied to many problems. Unfortunately, many of the nice properties and results that are available for Gaussian conditionals models are not transferable to non-Gaussian EFC models, and we need to develop adequate procedures for modeling, estimation, and inference for a generalized class of EFC models. Among a number of issues associated with such general EFC models, we are mainly concerned in this study with three problems: (1) developing a general procedure of MRF construction using multi-parameter exponential families, (2) application of the general procedure to a problem of spatial, categorical data analysis, and (3) investigating useful parameterizations of EFC models.