UCSC-SOE-17-02: Spatio-temporal modelling using integro-difference equations with bivariate stable kernels

Robert Richardson, Athanasios Kottas and Bruno Sanso
03/01/2017 02:54 PM
An integro-difference equation can be represented as a hierarchical spatio-temporal dynamic model using appropriate parameterizations. The dynamics of the process defined by an integro-difference equation depends on the choice of a bivariate kernel distribution, where more flexible shapes generally result in more flexible models. Under a Bayesian modelling framework, we consider the use of the stable family of distributions for the kernel, as they are infinitely divisible and offer a variety of tail behaviors, orientations and skewness. Many of the attributes of the bivariate stable distribution are controlled by a measure, which we model using a flexible Bernstein polynomial basis prior. The method is the first attempt to incorporate non-Gaussian kernels in a two-dimensional integro-difference equation model and will be shown to improve prediction over the Gaussian kernel model for a data set of Pacific sea surface temperatures.

Revised July 2020