Mathematics – Statistics Theory
Scientific paper
2005-08-15
Statistical Science 2007, Vol. 22, No. 3, 430-449
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/088342307000000113 the Statistical Science (http://www.imstat.org/sts/) by the Insti
Scientific paper
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.
Drton Mathias
Perlman Michael D.
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