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Graphical models for sparse data: graphical Gaussian models with vertex and edge symmetries. (English) Zbl 1147.62046

Brito, Paula (ed.), COMPSTAT 2008. Proceedings in computational statistics. 18th symposium held in Porto, Portugal, August 24–29, 2008. With CD-ROM. Heidelberg: Physica-Verlag (ISBN 978-3-7908-2083-6/pbk). 105-116 (2008).
Summary: The models we consider, generically denoted RCOX models, are a special class of graphical Gaussian models. In RCOX models specific elements of the concentration/partial correlation matrix can be restricted to being identical which reduces the number of parameters to be estimated. Thereby these models can be applied to problems where the number of variables is substantially larger than the number of samples. This paper outlines the fundamental concepts and ideas behind the models but focuses on model selection. Inference in RCOX models is facilitated by the R package gRc.
For the entire collection see [Zbl 1144.65002].

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
05C90 Applications of graph theory
05C15 Coloring of graphs and hypergraphs
62H99 Multivariate analysis

Software:

gRc; R
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