Potential approach in marginalizing Gibbs models

Given an undirected graph G or hypergraph potential H model for a given set of variables V, we introduce two marginalization operators for obtaining t he undirected graph G(A) or hypergraph H-A associated with a given subset A subset of V such that the marginal distribution of A factorizes according to G(A) or H-A, respectively. Finally, we illustrate the method by its appl ication to some practical examples. With them we show that potential approa ch allow defining a finer factorization or performing a more precise condit ional independence analysis than undirected graph models. Finally, we expla in connections with related works. (C) 1999 Elsevier Science Inc. All right s reserved.