Graphical Gaussian Models with Symmetries and algebraic combinatorics
|Affiliation:||University of Waterloo|
|Room:||Mathematics & Computer Building (MC) 5158|
Graphical Gaussian models with symmetries are statistical models which combine statistical independence relations with equality constraints on model parameters, and can be compactly represented by vertex and edge colored graphs . Of particular statistical interest are graphs whose colorings satisfy certain regularity conditions which ensure the represented models to have desirable statistical properties. Four such coloring regularities have been identified in the literature, with the structure of the corresponding model classes being described in . The structure of a fifth model class, characterized by invariance of equality constraints on matrix entries under matrix inversion, is still poorly understood and it is an open problem to identify the corresponding coloring regularity. In this talk I will review the results referred to above, and will present two open problems exhibiting relations to algebraic combinatorics, in particular to permutation groups, association schemes and Jordan algebras.
 Højsgaard, S. and S. Lauritzen (2008). Graphical Gaussian models with edge and vertex symmetries. J. R. Statist. Soc. B 70, 1005-1027.  Gehrmann, H. (2011). Lattices of graphical Gaussian models with symmetries. Symmetry 3, 653-679.
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