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Title: Bayesian inference for regression copulas Authors:  Michael Smith - University of Melbourne (Australia) [presenting]
Nadja Klein - Humboldt University Berlin (Germany)
Abstract: A new semi-parametric distributional regression smoother for continuous data is proposed which is based on a copula decomposition of the joint distribution of the vector of response values. The copula is high-dimensional and constructed by inversion of a pseudo regression, where the conditional mean and variance are non-parametric functions of the covariates modeled using Bayesian splines. By integrating out the spline coefficients, we derive an implicit copula that captures dependence as a smooth non-parametric function of the covariates, which we call a regression copula. We derive some of its properties, and show that the entire distribution including the mean and variance of the response from the copula model are also smooth nonparametric functions of the covariates. Even though the implicit copula cannot be expressed in closed form, we estimate it efficiently using both Hamiltonian Monte Carlo and variational Bayes methods. We illustrate the efficacy of these estimators and copula model for implicit copulas up to dimension 40,981.