Multiway Dependence in Exponential Family Conditional Distributions

Jaehyung Lee, Mark S. Kaiser and Noel Cressie

Journal of Multivariate Analysis, 2001, vol. 79, issue 2, 171-190

Abstract: Conditionally specified statistical models are frequently constructed from one-parameter 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. B36, 192-225) formulated exponential family "auto-models" and showed the form that one-parameter 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.

Keywords: Markov; random; fields; pairwise-only; dependence; spatial; dependence (search for similar items in EconPapers)
Date: 2001
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Citations: View citations in EconPapers (4)

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