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Lattices of Graphical Gaussian Models with Symmetries
Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK
Received: 1 April 2011; in revised form: 30 August 2011 / Accepted: 5 September 2011 / Published: 7 September 2011
Abstract: In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations,  introduced model classes which place equality restrictions on concentrations or partial correlations. The models can be represented by vertex and edge coloured graphs. The need for model selection methods makes it imperative to understand the structure of model classes. We identify four model classes that form complete lattices of models with respect to model inclusion, which qualifies them for an Edwards–Havránek model selection procedure . Two classes turn out most suitable for a corresponding model search. We obtain an explicit search algorithm for one of them and provide a model search example for the other.
Keywords: conditional independence; covariance selection; invariance; model selection; patterned covariance matrices; permutation symmetry
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Gehrmann, H. Lattices of Graphical Gaussian Models with Symmetries. Symmetry 2011, 3, 653-679.
Gehrmann H. Lattices of Graphical Gaussian Models with Symmetries. Symmetry. 2011; 3(3):653-679.
Gehrmann, Helene. 2011. "Lattices of Graphical Gaussian Models with Symmetries." Symmetry 3, no. 3: 653-679.