A model searching method based on marginal model structures

Abstract

Suppose that we are interested in modeling for a random vector X and that we are given a set of graphical decomposable models, G1, ⋯ , Gm, for subvectors of X each of which share some variables with at least one of the other models. Under the assumption that the model of X is graphical and decomposable, we propose an approach of searching for models of X based on the given decomposable graphical models. A main idea in this approach is that we combine G1, ⋯ , Gm using graphs of prime separators (section 2). When the true graphical model for the whole data is decomposable, prime separators in a marginal model are also prime separators in a maximal combined model of the marginal models. This property plays a key role in model-combination. The proposed approach is applied to searching for a model of 100 variables for illustration.