The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 5B (2009), 2808-2837.
Markov equivalence for ancestral graphs
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.
Ann. Statist., Volume 37, Number 5B (2009), 2808-2837.
First available in Project Euclid: 17 July 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 68T30: Knowledge representation 05C75: Structural characterization of families of graphs
Secondary: 68T37: Reasoning under uncertainty
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