Modeling copulas with Bayesian networks - Júnior, Willian Darwin (2021)
Bayesian networks are extensively studied in machine learning and there is a significant growing interest on copulas in scientific literature beyond Statistics, but it is still uncommon to join those conceptual artifacts. Our research proposes an initial stage approach for combining those concepts in probabilistic modeling by splitting the model in two coupled elements, individual marginal distributions and a copula, reserving the Bayesian network modeling only to the copula portion and liberating the marginal distributions modeling to be done by any chosen strategy according to the data, without interfering in the dependence modeling. We compared two different marginal modeling techniques for the first stage of the modeling: a standard Bayesian inference using Mont Carlo Markov chain (MCMC) and a sample reducing. The results showed good performance in both cases in the sense of preserving the same structure scoring tendency as the traditional approach for discrete Bayesian networks and pointed to the viability of modeling copulas using Bayesian networks for samples with enough number of instances, which was the premise of this research. For helping in the data analysis stage of the methodology, a general data analysis and visualization software tool, designated LPSCopModel, was developed for providing variables description and concordance indexes, MCMC parametric distribution fitting and an empirical copula profile as a first glance at the dependence structure.