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Title: Nested Markov models Authors:  Thomas Richardson - University of Washington (United States)
Robin Evans - University of Oxford (United Kingdom)
James Robins - Harvard University (United States)
Ilya Shpitser - Johns Hopkins University (United States) [presenting]
Abstract: Directed acyclic graph (DAG) models may be characterized in at least four different ways: via a factorization, the d-separation criterion, the moralization criterion, and the local Markov property. As pointed out previously, marginals of DAG models also imply equality constraints that are not conditional independences. The well-known Verma constraint is an example. We will describe, via a factorization and Markov properties, a statistical model that captures all equality constraints implied by a hidden variable DAG model, including Verma constraints, but not inequality constraints. A previous characterization of these constraint gives an alternative definition of the model. We will also show that the fixing operation used to define this model, an operation that generalizes conditioning, marginalization and applications of the g-formula, gives a particular simple characterization of identifiable causal effects in hidden variable graphical causal models.