Lattices of Graphical Gaussian Models with Symmetries

Details Lattices of Graphical Gaussian Models with Symmetries Lattices of Graphical Gaussian Models with Symmetries

2011-04-08

arxiv.org/abs/1104.1608v2

Symmetry 2011, 3, 653-679

Mathematics

Statistics Theory

29 pages, 18 figures. Restructured Section 5, results unchanged; added references in Section 6; amended example in Section 6.3

Scientific paper

10.3390/sym3030653

In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, model classes which place equality restrictions on concentrations or partial correlations have previously been introduced in the literature. 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-Havr\'anek 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.

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