Pair-copula Bayesian networks

Abstract. Pair-copula Bayesian networks (PCBNs) are a novel class of multivariate statistical models, which combine the distributional flexibility of pair-copula con-structions (PCCs) with the parsimony of conditional independence models associated with directed acyclic graphs (DAG). We are first to provide generic algorithms for random sampling and likelihood inference in arbitrary PCBNs as well as for selecting orderings of the parents of the vertices in the underlying graphs. Model selection of the DAG is facilitated using a version of the well-known PC algorithm which is based on a novel test for conditional independence of random variables tailored to the PCC framework. A simulation study shows the PC algorithm’s high aptitude for structure estimation in non-Gaussian PCBNs. The proposed methods are finally applied to modelling financial return data. Key words: Conditional independence test; copulas; directed acyclic graphs; graph-ical models; likelihood inference; PC algorithm; regular vines; structure estimation. 1