Spatiotemporal modelling using integro-difference equations with bivariate stable kernels

Robert Richardson, Athanasios Kottas, Bruno Sansó

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2020 · Volume 82 · Issue 5

Abstract

An integro-difference equation can be represented as a hierarchical spatiotemporal 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 behaviours, 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.

Keywords

Bernstein polynomials, Elliptically contoured stable distributions, Fourier series, Markov chain Monte Carlo methods, Semiparametric Bayesian modelling

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