  Pair-copula Bayesian networks (PCBNs) are a novel class of multivariate
statistical models, which combine the distributional flexibility of pair-copula
constructions (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.
