Constraints on Marginalised DAGs
Lunedý 7 maggio 2012, ore 15.00, Aula 201, Robin J. EVANS, - Statistical Laboratory, University of Cambridge
Introduce: Antonio Forcina, UniversitÓ di Perugia
Models defined by the global Markov property for directed acyclic graphs (DAGs) possess many nice properties, including a simple factorisation, graphical criteria for determining independences (d-separation/moralisation), and computational tractability. As is well known, however, DAG models are not closed under the operation of marginalisation, so marginalised DAGs (mDAGs) describe a much larger and less well understood class of models.
mDAG models can be represented by graphs with directed and bidirected edges, under a modest extension of Richardson's ADMGs. We describe the natural Markov property for mDAGs, which imposes observable conditional independences, 'dormant' independences (Verma constraints) and inequality constraints, and provide some results towards its characterisation. In particular we describe the Markov equivalence classes of mDAG models over 3 observed variables. We also give a constructive proof that when 2 observed variables are not joined by any edge (directed or bidirected), then this always induces some constraint on the observed joint distribution.
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