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Learning in Graphical Models pp 231–259Cite as

Chain Graphs and Symmetric Associations

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Part of the book series: NATO ASI Series ((ASID,volume 89))

Abstract

Graphical models based on chain graphs, which admit both directed and undirected edges, were introduced by by Lauritzen, Wermuth and Frydenberg as a generalization of graphical models based on undirected graphs, and acyclic directed graphs. More recently Andersson, Madigan and Perlman have given an alternative Markov property for chain graphs. This raises two questions: How are the two types of chain graphs to be mterpreted? In which situations should chain graph models be used and with which Markov property?

The undirected edges in a chain graph are often said to represent ‘symmetric’ relations. Several different symmetric structures are considered, and it is shown that although each leads to a different set of conditional independences, none of those considered corresponds to either of the chain graph Markov properties.

The Markov properties of undirected graphs, and directed graphs, including latent variables and selection variables, are compared to those that have been proposed for chain graphs. It is shown that there are qualitative differences between these Markov properties. As a corollary, it is proved that there are chain graphs which do not correspond to any cyclic or acyclic dlirected graph, even with latent or selection variables.

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Authors and Affiliations

  1. Statistics Department, University of Washington, USA

    Thomas S. Richardson

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  1. Thomas S. Richardson
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Editors and Affiliations

  1. Massachusetts Institute of Technology, E25-229, Cambridge, MA, 02139, USA

    Michael I. Jordan

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© 1998 Springer Science+Business Media Dordrecht

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Richardson, T.S. (1998). Chain Graphs and Symmetric Associations. In: Jordan, M.I. (eds) Learning in Graphical Models. NATO ASI Series, vol 89. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5014-9_9

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  • DOI: https://doi.org/10.1007/978-94-011-5014-9_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6104-9

  • Online ISBN: 978-94-011-5014-9

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