A kernel-based spectral model for non-Gaussian spatio-temporal processes

Spatio-temporal processes can often be written as hierarchical state-space processes. In situations with complicated dynamics such as wave propagation, it is difficult to parameterize state transition functions for high-dimensional state processes. Although in some cases prior understanding of the physical process can be used to formulate models for the state transition, this is not always possible. Alternatively, for processes where one considers discrete time and continuous space, complicated dynamics can be modeled by stochastic integro-difference equations in which the associated redistribution kernel is allowed to vary with space and/or time. By considering a spectral implementation of such models, one can formulate a spatio-temporal model with relatively few parameters that can accommodate complicated dynamics. This approach can be developed in a hierarchical framework for non-Gaussian processes, as demonstrated on cloud intensity data.