Open Access
October 2009 Markov equivalence for ancestral graphs
R. Ayesha Ali, Thomas S. Richardson, Peter Spirtes
Ann. Statist. 37(5B): 2808-2837 (October 2009). DOI: 10.1214/08-AOS626


Ancestral graphs can encode conditional independence relations that arise in directed acyclic graph (DAG) models with latent and selection variables. However, for any ancestral graph, there may be several other graphs to which it is Markov equivalent. We state and prove conditions under which two maximal ancestral graphs are Markov equivalent to each other, thereby extending analogous results for DAGs given by other authors. These conditions lead to an algorithm for determining Markov equivalence that runs in time that is polynomial in the number of vertices in the graph.


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R. Ayesha Ali. Thomas S. Richardson. Peter Spirtes. "Markov equivalence for ancestral graphs." Ann. Statist. 37 (5B) 2808 - 2837, October 2009.


Published: October 2009
First available in Project Euclid: 17 July 2009

zbMATH: 1178.68574
MathSciNet: MR2541448
Digital Object Identifier: 10.1214/08-AOS626

Primary: 05C75 , 68T30
Secondary: 68T37

Keywords: directed acyclic graphs , discriminating path , inducing path , Markov equivalence , polynomial-time algorithm

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 5B • October 2009
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