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 the undirected graph GA or hypergraph HA associated with a given subset A V such that the marginal distribution of A factorizes according to GA or HA, respectively. Finally, we illustrate the method by its application to some practical examples. With them we show that potential approach allow de®ning a ®ner factorization or performing a more precise conditional independence analysis than undirected graph models. Finally, we explain connections with related works. Ó 1999 Elsevier Science Inc. All rights reserved.