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Biometrika 2004 91(1):234-239; doi:10.1093/biomet/91.1.234
© 2004 by Biometrika Trust
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Miscellanea

Compatibility among marginal densities

Yuchung J.Wang1

1 Department of Mathematical Sciences, Rutgers University, Camden, New Jersey 08102, U.S.Ayuwang{at}crab.rutgers.edu

In the Lancaster representation a joint density is decomposed into a sum of additive interactions.Using these interactions, we derive conditions for checking compatibility among a collection of marginal densities. The representation also shows how to construct an all-positive joint density additively from a given set of compatible marginals. An algorithm is proposed for reducing the dimension of the marginal densities so that compatibility can be checked in sequential increments. The representation may yield insights into the construction and simulation of models represented by undirected graphs.

Key Words: Additive interactions; Generating class; Lancaster's representation; Reproducible; Undirected graph

Received June 2002. Revised February 2003


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