Dynamical non-Gaussian modelling of spatial processes

Environmental data are often assumed to follow a spatio-temporal Gaussian process, possibly after transformation. However, heterogeneity might have a pattern not accommodated by transformation and modelling the variance laws is an appealing alternative. This work extends the multivariate dynamic Gaussian model by defining the process as a scale mixture with the scale depending on covariates. State-space equations define the temporal dynamics, resulting in feasible inference and prediction. Various simulations studies show that the parameters are identifiable and our proposal recovers simpler structures. The analyses of temperature and ozone illustrate the improvement in quantifying the uncertainty of predictions.