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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.

In genetic studies of complex diseases, it is important to identify and qualify gene-gene interactions. Interaction is often defined as deviance from genetic additive effects. But this statistical definition needs not to reflect the genes' biological interactions. I propose a new method to detect gene-gene interaction that exploits the concept of synergy and antagonism, which is said to capture biological relationships. The conditional synergy index (CSI) classifies and quantifies interaction on the penetrance scale. The general theory under two-locus disease models is developed. The index assumes a cohort design and genotypes to be dichotomized into risk-genotypes (exposed) and non-risk-genotypes (unexposed) but it does not assume the loci to be in linkage equilibrium. In simulation studies the performance of the CSI, its estimator and variance is investigated and compared to the performance of various epidemiological interaction measure like e.g. Rothman's syngergy index and to appropriate bootstrap estimators. The results exhibit that in contrast to common interaction measures, only the CSI is adequat to detect interaction on the penetrance scale. However, the proposed estimator of the CSI shows a slow convergence.