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Bayesian MAP model selection of chain event graphs

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  • Freeman, G.
  • Smith, J.Q.

Abstract

Chain event graphs are graphical models that while retaining most of the structural advantages of Bayesian networks for model interrogation, propagation and learning, more naturally encode asymmetric state spaces and the order in which events happen than Bayesian networks do. In addition, the class of models that can be represented by chain event graphs for a finite set of discrete variables is a strict superset of the class that can be described by Bayesian networks. In this paper we demonstrate how with complete sampling, conjugate closed form model selection based on product Dirichlet priors is possible, and prove that suitable homogeneity assumptions characterise the product Dirichlet prior on this class of models. We demonstrate our techniques using two educational examples.

Suggested Citation

  • Freeman, G. & Smith, J.Q., 2011. "Bayesian MAP model selection of chain event graphs," Journal of Multivariate Analysis, Elsevier, vol. 102(7), pages 1152-1165, August.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:7:p:1152-1165
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    1. Heard, Nicholas A. & Holmes, Christopher C. & Stephens, David A., 2006. "A Quantitative Study of Gene Regulation Involved in the Immune Response of Anopheline Mosquitoes: An Application of Bayesian Hierarchical Clustering of Curves," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 18-29, March.
    2. James E. Smith & Samuel Holtzman & James E. Matheson, 1993. "Structuring Conditional Relationships in Influence Diagrams," Operations Research, INFORMS, vol. 41(2), pages 280-297, April.
    3. Yael Berstein & Hugo Maruri-Aguilar & Shmuel Onn & Eva Riccomagno & Henry Wynn, 2010. "Minimal average degree aberration and the state polytope for experimental designs," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 673-698, August.
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    1. Manuele Leonelli & Eva Riccomagno & Jim Q. Smith, 2020. "Coherent combination of probabilistic outputs for group decision making: an algebraic approach," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 42(2), pages 499-528, June.

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