For random elements X and Y (e.g. vectors) a complete characterization of their association is given in terms of an odds ratio function. The main result establishes for any odds ratio function and any pre-specified marginals the unique existence of a corresponding joint distribution (the joint...

Considering the covariance selection problem of multivariate normal distributions, we show that its Fenchel dual formulation is insightful and allows one to calculate direct estimates under decomposable models. We next generalize the covariance selection to multivariate dependence, which...