Bayesian Regularized Regression Copula Processes for Multivariate Responses.

AbstractWe propose a new distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a “regression copula process”. To allow for large covariate vectors the regression coefficients are regularized using a novel multivariate extension of the horseshoe prior. Bayesian inference and distributional predictions are evaluated using efficient variational inference methods, allowing application to large datasets. An advantage of the approach is that the marginal distributions of the response vector can be estimated separately and accurately, resulting in predictive distributions that are marginally calibrated. Two applications of the methodology illustrate its efficacy. The first is the econometric modeling and prediction of half-hourly regional Australian electricity prices. The second is the evaluation of multivariate posteriors in likelihood-free inference (LFI) for a model of tree species abundance. This extends a previous univariate regression copula LFI method for evaluating univariate posteriors. In both applications, we demonstrate that our new approach exhibits a desirable marginal calibration property. [ABSTRACT FROM AUTHOR]