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Spatiotemporal modelling using integro‐difference equations with bivariate stable kernels
Author(s) -
Richardson Robert,
Kottas Athanasios,
Sansó Bruno
Publication year - 2020
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12393
Subject(s) - bivariate analysis , mathematics , kernel (algebra) , skewness , bayesian probability , distribution (mathematics) , measure (data warehouse) , gaussian , statistics , mathematical analysis , computer science , data mining , discrete mathematics , physics , quantum mechanics
Summary 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.