  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.
