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Multiway Dependence in Exponential Family Conditional Distributions

✍ Scribed by Jaehyung Lee; Mark S. Kaiser; Noel Cressie

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
177 KB
Volume
79
Category
Article
ISSN
0047-259X

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✦ Synopsis

Conditionally specified statistical models are frequently constructed from oneparameter exponential family conditional distributions. One way to formulate such a model is to specify the dependence structure among random variables through the use of a Markov random field (MRF). A common assumption on the Gibbsian form of the MRF model is that dependence is expressed only through pairs of random variables, which we refer to as the pairwise-only dependence'' assumption. Based on this assumption, J. Besag (1974, J. Roy. Statist. Soc. Ser. B 36, 192 225) formulated exponential family auto-models'' and showed the form that oneparameter exponential family conditional densities must take in such models. We extend these results by relaxing the pairwise-only dependence assumption, and we give a necessary form that one-parameter exponential family conditional densities must take under more general conditions of multiway dependence. Data on the spatial distribution of the European corn borer larvae are fitted using a model with Bernoulli conditional distributions and several dependence structures, including pairwise-only, three-way, and four-way dependencies.

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