Bayesian networks are powerful graphical models that capture the probabilistic dependencies between random variables. Pair-copula Bayesian networks (Bauer et al. 2011) extend the well-known Gaussian Bayesian networks by allowing for non-Gaussian distributions through the incorporation of bivariate copulas and univariate marginal distributions into the network structure. A widely used method for learning the structure of Bayesian networks is the constraint-based PC algorithm (Spirtes et al. 1993), which employs conditional independence tests to identify the absence of edges in an underlying directed acyclic graph (DAG). In the case of continuous data, Fisher’s Z-test of partial correlation is commonly used as a benchmark for testing conditional independencies. However, a significant limitation of this approach is its reliance on the assumption of a multivariate Gaussian distribution, under which partial and conditional correlations coincide, and vanishing correlations imply independence. To overcome this limitation, a novel conditional independence test based on Y-vine copulas is introduced. Y-vine copulas, a subclass of regular vine copulas introduced by Tepegjozova and Czado (2023), are designed to model bivariate conditional distributions using only univariate distributions and bivariate copulas, thus avoiding the need for integration. Their inherent flexibility allows them to model data without making assumptions about the underlying distribution. The modified PC algorithm, utilizing Y-vines to facilitate conditional independence testing, will be evaluated against its traditional counterpart in a simulation study using both Gaussian and non-Gaussian data generated from Bayesian networks. To produce non-Gaussian data, a new simulation procedure based on D-vines is proposed, which enables approximate sampling from a pair-copula Bayesian network without imposing constraints on the underlying structure or the order of the parent nodes. The results of the simulation study highlight that the Y-vine-based PC algorithm more accurately recovers the true underlying graphical structure than the Z-test benchmark, albeit with significantly increased computational effort. Finally, it will be demonstrated that univariate D-vine-based regression can effectively learn the parent order of a node and parameters in pair-copula Bayesian networks. The combination of the Y-vine-based PC algorithm and the D-vine-based parameter learning method will be applied to estimate pair-copula Bayesian networks in real-world case studies.     «

Bayesian networks are powerful graphical models that capture the probabilistic dependencies between random variables. Pair-copula Bayesian networks (Bauer et al. 2011) extend the well-known Gaussian Bayesian networks by allowing for non-Gaussian distributions through the incorporation of bivariate copulas and univariate marginal distributions into the network structure. A widely used method for learning the structure of Bayesian networks is the constraint-based PC algorithm (Spirtes et al. 1993)...     »