Preprint #96-30
The Construction of Multivariate Distributions from
Markov Random Fields
by
Mark S. Kaiser and Noel Cressie
Abstract
We address the problem of constructing and identifying a valid joint
probability density function from a set of specified conditional densities.
The approach taken is based on the development of relations between
the joint and the conditional densities using Markov random fields.
We give a necessary and sufficient condition on the support sets of the
random variables to allow these relations to be developed. This
condition, which we call the Markov random field support condition,
supercedes a common assumption known generally as the positivity
condition. We show how these relations may be used in reverse order to
construct a valid model from specification of conditional densities
alone. The constructive process, and the role of conditions needed for
its application, are illustrated with several simple examples.
Copies of preprints are available from the author upon request. Use
the preprint number (located at the top of the page) and
make the request directly to the author, Iowa State
University,
Department of Statistics, Snedecor Hall, Ames, IA 50011-1210.