MARKOV EQUIVALENCE FOR ANCESTRAL GRAPHS

• 成果类型: Article
• 署名作者: Ali, R. Ayesha; Richardson, Thomas S.; Spirtes, Peter
• 署名单位: University of Guelph; University of Washington; University of Washington Seattle; Carnegie Mellon University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS626
• 发表日期: 2009
• 页码: 2808-2837
• 关键词: seemingly unrelated regressions; conditional-independence; models

摘要

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.