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Symmetry 2011, 3(3), 653-679; doi:10.3390/sym3030653

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 / Revised: 30 August 2011 / Accepted: 5 September 2011 / Published: 7 September 2011
(This article belongs to the Special Issue Symmetry in Probability and Inference)
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Abstract

In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, [1] 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 [2]. 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 conditional independence; covariance selection; invariance; model selection; patterned covariance matrices; permutation symmetry
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Gehrmann, H. Lattices of Graphical Gaussian Models with Symmetries. Symmetry 2011, 3, 653-679.

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