Separation and completeness properties for AMP chain graph Markov models

• 成果类型: Article
• 署名作者: Levitz, M; Perlman, MD; Madigan, D
• 署名单位: University of Washington; University of Washington Seattle; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 1751-1784
• 关键词: acyclic digraphs; equivalence classes; Bayesian networks; INDEPENDENCE; KNOWLEDGE

摘要

Pearl's well-known d-separation criterion for an acyclic directed graph (ADG) is a pathwise separation criterion that can be used to efficiently identify all valid conditional independence relations in the Markov model determined by the graph. This paper introduces p-separation, a pathwise separation criterion that efficiently identifies all valid conditional independences under the Andersson-Madigan-Perlman (AMP) alternative Markov property for chain graphs (= adicyclic graphs), which include both ADGs and undirected graphs as special cases, The equivalence of p-separation to the augmentation criterion occurring in the AMP global Markov property is established, and p-separation is applied to prove completeness of the global Markov property for AMP chain graph models. Strong completeness of the AMP Markov property is established, that is, the existence of Markov perfect distributions that satisfy those and only those conditional independences implied by the AMP property (equivalently, by p-separation). A linear-time algorithm for determining p-separation is presented.