A Relationship between a Graphical Model and Its Marginal Models

S.-H. Kim (South Korea)


conditional independence; edge-subgraph; factorized; globally Markov; Markovian subgraph; undirected graph.


Consider a graphical model of a random vector XV whose model structure is represented by an undirected graph G and suppose that we are given a set, say S, of marginal models of the graphical model. Provided that each com ponent of XV is involved in at least one of the marginal models, it is shown in this paper that the set of the mod els which are Markov with respect to G is contained in the set of the models each of which has marginals which are Markov with respect to the interaction graphs of the marginals in S.

Important Links:

Go Back