Journal
ANNALS OF STATISTICS
Volume 37, Issue 5B, Pages 2808-2837Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/08-AOS626
Keywords
Directed acyclic graphs; discriminating path; inducing path; Markov equivalence; polynomial-time algorithm
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Funding
- National University of Singapore
- NSERC [RG326951-06]
- William and Flora Hewlett Foundation
- NSF [DMS-99-72008, DMS-05-05865]
- EPA [CR 827970-01-0]
- NIH [R01 AI032475]
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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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