STRUCTURAL MARKOV GRAPH LAWS FOR BAYESIAN MODEL UNCERTAINTY

• 成果类型: Article
• 署名作者: Byrne, Simon; Dawid, A. Philip
• 署名单位: University of London; University College London; University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/15-AOS1319
• 发表日期: 2015
• 页码: 1647-1681
• 关键词: conditional-independence; decomposable graphs; equivalence classes; chain

摘要

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov properties, for both undirected decomposable and directed acyclic graphs, which requires that the structure of distinct components of the graph be conditionally independent given the existence of a separating component. This allows the analysis and comparison of multiple graphical structures, while being able to take advantage of the common conditional independence constraints. Moreover, we show that these properties characterise exponential families, which form conjugate priors under sampling from compatible Markov distributions.