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A Note on Equivalence Classes of Directed Acyclic Independence Graphs

Published online by Cambridge University Press:  27 July 2009

David Madigan
David Madigan
Affiliation:
Department of Statistics, GN-22, University of Washington, Seattle, Washington 98195
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Extract

Directed acyclic independence graphs (DAIGs) play an important role in recent developments in probabilistic expert systems and influence diagrams (Chyu [1]). The purpose of this note is to show that DAIGs can usefully be grouped into equivalence classes where the members of a single class share identical Markov properties. These equivalence classes can be identified via a simple graphical criterion. This result is particularly relevant to model selection procedures for DAIGs (see, e.g., Cooper and Herskovits [2] and Madigan and Raftery [4]) because it reduces the problem of searching among possible orientations of a given graph to that of searching among the equivalence classes.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 7 , Issue 3 , July 1993 , pp. 409 - 412
Copyright
Copyright © Cambridge University Press 1993

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References

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