A relationship between a graphical model and its marginal models

  • Authors:

  • Sung-Ho Kim

  • Affiliations:

  • Division of Applied Mathematics, Korea Advanced Institute of Science and Technology, Daejeon, South Korea

  • Venue:
  • MIC'06 Proceedings of the 25th IASTED international conference on Modeling, indentification, and control
  • Year:
  • 2006

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Abstract

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 component of Xv is involved in at least one of the marginal models, it is shown in this paper that the set of the models 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.