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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, December 3, 2002}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Michael Perlman}
\centerline{\sl University of Washington}
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\centerline{\bf Markov equivalence and essential graphs for graphical Markov models}
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Graphical Markov models (GMM) use graphs, either undirected, directed,
or
mixed, to represent global dependences among statistical variables by
means of local specifications, thereby achieving substantial computation
efficiencies. Examples of GMMs include (finite) Markov random fields,
Bayesian networks, and influence diagrams. We shall review the basic
Markov properties of GMMs determined by undirected graphs, acyclic
directed graphs, and adicyclic graphs = "chain graphs",
which allow both undirected and directed edges with no partially
directed
cycles, and briefly discuss their statistical analysis. Three topics of
current interest will be noted: characterizing Markov-equivalent graphs,
unique representation of a Markov equivalence class by means of its
"essential graph", and the existence of competing Markov interpretations
of the same chain graph.


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