The Annals of Statistics

Markov equivalence for ancestral graphs

R. Ayesha Ali, Thomas S. Richardson, and Peter Spirtes

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Abstract

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.

Article information

Source
Ann. Statist., Volume 37, Number 5B (2009), 2808-2837.

Dates
First available in Project Euclid: 17 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.aos/1247836670

Digital Object Identifier
doi:10.1214/08-AOS626

Mathematical Reviews number (MathSciNet)
MR2541448

Zentralblatt MATH identifier
1178.68574

Subjects
Primary: 68T30: Knowledge representation 05C75: Structural characterization of families of graphs
Secondary: 68T37: Reasoning under uncertainty

Keywords
Directed acyclic graphs discriminating path inducing path Markov equivalence polynomial-time algorithm

Citation

Ali, R. Ayesha; Richardson, Thomas S.; Spirtes, Peter. Markov equivalence for ancestral graphs. Ann. Statist. 37 (2009), no. 5B, 2808--2837. doi:10.1214/08-AOS626. https://projecteuclid.org/euclid.aos/1247836670


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References

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