Bayesian nonparametric approach for vine copula modelling: an application to preterm birth data in repeated pregnancies

Preterm births represent a serious medical issue since they can affect the health of the mother and the fetus. Our idea is to study the dependence between preterm births in repeated pregnancies using a vine copula approach. More precisely, we model marginals with generalized additive models for location scale and shape (GAMLSS) and we follow a Bayesian nonparametric approach to estimate the pair copulas in the vine. Our approach has two main advantages compared to the traditional methods: on the one hand it is extremely flexible, due to the vine structure, and on the other hand it overcomes the need of specify the families of each pair copula.