NESTED MARKOV PROPERTIES FOR ACYCLIC DIRECTED MIXED GRAPHS

• 成果类型: Article
• 署名作者: Richardson, Thomas S.; Evans, Robin J.; Robins, James M.; Shpitser, Ilya
• 署名单位: University of Washington; University of Washington Seattle; University of Oxford; Harvard University; Johns Hopkins University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/22-AOS2253
• 发表日期: 2023
• 页码: 334-361
• 关键词: CAUSAL; margins

摘要

Conditional independence models associated with directed acyclic graphs (DAGs) may be characterized in at least three different ways: via a factorization, the global Markov property (given by the d-separation crite-rion), and the local Markov property. Marginals of DAG models also imply equality constraints that are not conditional independences; the well-known ???Verma constraint??? is an example. Constraints of this type are used for testing edges, and in a computationally efficient marginalization scheme via variable elimination. We show that equality constraints like the ???Verma constraint??? can be viewed as conditional independences in kernel objects obtained from joint distributions via a fixing operation that generalizes conditioning and marginalization. We use these constraints to define, via ordered local and global Markov properties, and a factorization, a graphical model associated with acyclic directed mixed graphs (ADMGs). We prove that marginal distri-butions of DAG models lie in this model, and that a set of these constraints given by Tian provides an alternative definition of the model. Finally, we show that the fixing operation used to define the model leads to a particularly simple characterization of identifiable causal effects in hidden variable causal DAG models.