Compatibility among marginal densities

Abstract

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. © 2004 Biometrika Trust.