Preprint #96-17
Multiway Dependence in Exponential Family Conditional
Distributions
by
Jaehyung Lee, Mark S. Kaiser and Noel Cressie
Abstract
Conditionally specified statistical models are frequently constructed from
conditional one-parameter exponential family 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. When this is done, a
common assumption is that dependence is expressed only through pairs of random
variables, the `pairwise-only dependence' assumption. Using a Markov random
field structure and the pairwise-only dependence assumption, Besag (1974)
formulated exponential family `auto-models', and showed the form that
conditional one-parameter exponential family densities must have in such
models. We extend those results under relaxation of the pairwise-only
dependence assumption, and give a necessary form for conditional
one-parameter exponential family densities under more general conditions
of multiway dependence.
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University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.