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Multiple testing and error control in Gaussian graphical model selection. (English) Zbl 1246.62143

Summary: Graphical models provide a framework for exploration of multivariate dependence patterns. The connection between graphs and statistical models is made by identifying the vertices of the graph with the observed variables and translating the patterns of edges in the graphs 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.

MSC:

62H15 Hypothesis testing in multivariate analysis
62H20 Measures of association (correlation, canonical correlation, etc.)
05C90 Applications of graph theory
05C20 Directed graphs (digraphs), tournaments
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