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Ancestral graph Markov models. (English) Zbl 1033.60008
Summary: This paper introduces a class of graphical independence models that is closed under marginalization and conditioning but that contains all DAG independence models. This class of graphs, called maximal ancestral graphs, has two attractive features: there is at most one edge between each pair of vertices; every missing edge corresponds to an independence relation. These features lead to a simple parameterization of the corresponding set of distributions in the Gaussian case.

MSC:
60C05Combinatorial probability
05C20Directed graphs (digraphs), tournaments
62M45Neural nets and related approaches (inference from stochastic processes)
68R10Graph theory in connection with computer science (including graph drawing)
68T30Knowledge representation
Software:
Amos; BMDP; LISREL; SAS
WorldCat.org
Full Text: DOI Euclid
References:
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[63] SEATTLE, WASHINGTON 98195 E-MAIL: tsr@stat.washington.edu INSTITUTE FOR HUMAN & MACHINE COGNITION 40 SOUTH ALCANIZ PENSACOLA, FLORIDA 32501 E-MAIL: ps7z@andrew.cmu.edu