Acyclic Linear SEMs Obey the Nested Markov Property.

ABSTRACT: The conditional independence structure induced on the observed marginal distribution by a hidden variable directed acyclic graph (DAG) may be represented by a graphical model represented by mixed graphs called maximal ancestral graphs (MAGs). This model has a number of desirable properties, in particular the set of Gaussian distributions can be parameterized by viewing the graph as a path diagram. Models represented by MAGs have been used for causal discovery [22], and identification theory for causal effects [28]. In addition to ordinary conditional independence constraints, hidden variable DAGs also induce generalized independence constraints. These constraints form the nested Markov property [20]. We first show that acyclic linear SEMs obey this property. Further we show that a natural

SUBMITTER: Shpitser I 

PROVIDER: S-EPMC6461354 | biostudies-literature | 2018 Aug

REPOSITORIES: biostudies-literature