Pair-copula Bayesian networks

TL;DR

This paper introduces Pair-copula Bayesian networks (PCBNs), a flexible multivariate modeling framework combining pair-copula constructions with Bayesian network structures, and provides algorithms for inference, sampling, and structure learning.

Contribution

It is the first to develop generic algorithms for sampling, likelihood inference, and structure learning in PCBNs, enhancing modeling flexibility for complex dependencies.

Findings

The PC algorithm effectively estimates structures in non-Gaussian PCBNs.

Simulation studies demonstrate high accuracy of structure estimation.

Application to financial data shows practical utility of PCBNs.

Abstract

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.