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August 2007 Multiple Testing and Error Control in Gaussian Graphical Model Selection
Mathias Drton, Michael D. Perlman
Statist. Sci. 22(3): 430-449 (August 2007). DOI: 10.1214/088342307000000113


Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graph and statistical model is made by identifying the vertices of the graph with the observed variables and translating the pattern of edges in the graph into a pattern of conditional independences that is imposed on the variables’ joint distribution. Focusing on Gaussian models, we review classical graphical models. For these models the defining conditional independences are equivalent to vanishing of certain (partial) correlation coefficients associated with individual edges that are absent from the graph. Hence, Gaussian graphical model selection can be performed by multiple testing of hypotheses about vanishing (partial) correlation coefficients. We show and exemplify how this approach allows one to perform model selection while controlling error rates for incorrect edge inclusion.


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Mathias Drton. Michael D. Perlman. "Multiple Testing and Error Control in Gaussian Graphical Model Selection." Statist. Sci. 22 (3) 430 - 449, August 2007.


Published: August 2007
First available in Project Euclid: 2 January 2008

zbMATH: 1246.62143
MathSciNet: MR2416818
Digital Object Identifier: 10.1214/088342307000000113

Keywords: acyclic directed graph , Bayesian network , bidirected graph , chain graph , concentration graph , covariance graph , DAG , Graphical model , multiple testing , undirected graph

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.22 • No. 3 • August 2007
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