Characterizing Markov equivalence classes for AMP chain graph models

• 成果类型: Article
• 署名作者: Andersson, Steen A.; Perlman, Michael D.
• 署名单位: Indiana University System; Indiana University Bloomington; University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000173
• 发表日期: 2006
• 页码: 939-972
• 关键词: acyclic digraphs; PROPERTY

摘要

Chain graphs (CG) (= adicyclic graphs) use undirected and directed edges to represent both structural and associative dependences. Like acyclic directed graphs (ADGs), the CG associated with a statistical Markov model may not be unique, so CG(S) fall into Markov equivalence classes, which may be superexponentially large, leading to unidentifiability and computational inefficiency in model search and selection. It is shown here that, under the Andersson-Madigan-Perlman (AMP) interpretation of a CG, each Markovequivalence class can be uniquely represented by a single distinguished CG, the AMP essential graph, that is itself simultaneously Markov equivalent to all CGs in the AMP Markov equivalence class. A complete characterization of AMP essential graphs is obtained. Like the essential graph previously introduced for ADGs, the AMP essential graph will play a fundamental role for inference and model search and selection for AMP CG models.