Markovian Combination of Graphical Model Structures of Undirected Graphs

S.-H. Kim (Korea)

Keywords

combined model structure; graphseparateness; interac tion graph; Markovian subgraph; prime separator; self connected separator.

Abstract

Suppose that we are interested in modeling for a random vector X and that we are given a set of graphical 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, we propose an approach of searching for model structures of X based on the given graphical models. A main idea in this approach is that we combine G1, · · · , Gm in three steps, union, check of separateness, and check of marginalization. These three steps of operation yield models structures which are max imal in the context of set-inclusion of edges. A simulated example strongly recommends the proposed approach.

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