  We introduce a mixture-model of beta distributions to identify significant
correlations among $P$ predictors when $P$ is large. The method relies on
theorems in convex geometry, which we use to show how to control the error rate
of edge detection in graphical models. Our `betaMix' method does not require
any assumptions about the network structure, nor does it assume that the
network is sparse. The results in this article hold for a wide class of data
generating distributions that include light-tailed and heavy-tailed spherically
symmetric distributions.
