Copula directed acyclic graphs

We present a new methodology for selecting a Bayesian network for continuous data outside the widely used class of multivariate normal distributions. The use of bivariate copula densities to model connections between pairs of nodes in the network brings in flexibility in the choice of the distribution. Cand D-vines play a central role in dealing with the high-dimensional aspect of the data, due to the fact that these decompositions of a multivariate density employ a series of bivariate conditional copulas to represent a general multivariate density. We thus combine directed acyclic graphs (DAGs) and their associated probability model with copula C/D-vines in order to construct ‘copula based DAGs’, or in short ‘cDAGs’. We also present a new criterion for graph selection tailored to the joint modeling of data based on graphs and copulas. This is joint work with Eugen Pircalabelu and Irene Gijbels.