A hierarchical bi-resolution spatial skew-t model

Advances in Gaussian methodology for spatio-temporal data have made it possible to develop sophisticated non-stationary models for very large data sets. The literature on non-Gaussian spatio-temporal models is comparably sparser and strongly focused on distributing the uncertainty across layers of a hierarchical model. This choice allows to model the data conditionally, to transfer the dependence structure at the process level via a link function, and to use the familiar Gaussian framework. Conditional modeling, however, implies an (unconditional) distribution function that can only be obtained through integration of the latent process, with a closed form only in special cases. In this work, we present a spatio-temporal non-Gaussian model that assumes an (unconditional) skew- data distribution, but also allows for a hierarchical representation by defining the model as the sum of a small and a large scale spatial latent effect. We provide semi-closed form expressions for the steps of the Expectation-Maximization algorithm for inference, as well as the conditional distribution for spatial prediction. We demonstrate how it outperforms a Gaussian model in a simulation study, and show an example of application to precipitation data in Colorado.