Dynamical non-Gaussian modelling of spatial processes

TL;DR

This paper introduces a flexible non-Gaussian model for spatio-temporal environmental data by combining Gaussian and log-Gaussian processes with dynamic variance modeling, improving uncertainty quantification.

Contribution

It extends the Multivariate Dynamic Gaussian model with a scale mixture approach, allowing for non-Gaussian features and covariate-dependent variance over space and time.

Findings

Parameters are identifiable in artificial data

Model recovers simpler structures effectively

Improves uncertainty quantification in environmental predictions

Abstract

Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by transforming the data. In this scenario, modelling the variance laws is an appealing alternative. This work adds flexibility to the usual Multivariate Dynamic Gaussian model by defining the process as a scale mixture between a Gaussian and log-Gaussian processes. The scale is represented by a process varying smoothly over space and time which is allowed to depend on covariates. State-space equations define the dynamics over time for both mean and variance processes resulting infeasible inference and prediction. Analysis of artificial datasets show that the parameters are identifiable and simpler models are well recovered by the general proposed model. The analyses of two important environmental processes, maximum temperature and maximum ozone, illustrate the effectiveness of our proposal in improving the uncertainty quantification in the prediction of spatio-temporal processes.