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Graphical Gaussian Models with Edge and Vertex Symmetries

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Graphical Gaussian Models are typically defined through restricting elements of the inverse covariance matrix, aka the concentration matrix, to be equal to zero; this corresponds to conditional independence restrictions of an undirected graph determined by absence of edges between pairs of variables with zero joint concentration. In this way, complex multivariate distributions may be described with parsimony. This lecture is concerned with further restrictions on the distribution determined by symmetry; the symmetry restrictions are obtained by partitioning the vertex set into vertex colour classes and the edge set into edge colour classes so that parameters corresponding to objects in the same colour class are restricted to be identical. The lecture will describe examples of such models and discuss their properties. The material presented is based on joint work with Sren Hjsgaard and Helene Neufeld.

This talk is part of the Statistics series.

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