Distributional copula regression for space-time data

A07 develops novel models for multivariate spatio-temporal data using distributional copula regression. Of particular interest are tests for the significance of predictors and automatic variable selection using Bayesian selection priors. In the long run, the project will consider computationally efficient modeling of non-stationary dependencies using stochastic partial differential equations.

Modeling dependencies in space-time data is of interest for several projects of TRR 391 and copulas are an important mathematical tool to capture such potentially complex associations. In this project, we will develop novel models for multivariate spatio-temporal data based on copulas and distributional regression. In particular we leverage the potential of statistical testing and Bayesian shrinkage priors to induce sparse yet flexibly varying dependence structures between multiple outcomes that are observed over space and time. With the help of distributional regression it will be possible to describe the entire conditional distributions - including the dependence structure - as functions of space, time and potentially further covariates. To find a reasonable model we will construct statistical tests to determine the copula specification on the one hand, and complement these on the other hand by  automatic variable selection using Bayesian variable selection priors. The latter will be particularly appealing to allow for hierarchical model specifications and modular estimation in potentially high-dimensional spatio-temporal copula regression models. Estimation is planned to be conducted by variational inference and generalized Bayesian methods. In a long-term perspective we will consider modeling the dependence structures non-stationary, handle irregularly observed and missing space-time data and leverage the potential of deep learning methods to capture high-dimensional interactions of the joint covariate, space and time domains more thoroughly.