Spatial process modelling for univariate and multivariate dynamic spatial data

TLDR

Spatiotemporal modelling literature is extensive, and this work considers continuous spatial domains with discrete time. The study aims to develop dynamic spatial models that are flexible, tractable, and support general mean structures and non‑stationary associations. The authors propose spatiotemporally varying coefficient models for univariate data, coregionalized multivariate spatial processes, and a Bayesian inference framework, applying them to Colorado climate data. Posterior and predictive inference yields tables and maps that illustrate spatiotemporal patterns and uncertainty. © 2005 John Wiley & Sons, Ltd.

Abstract

Abstract There is a considerable literature in spatiotemporal modelling. The approach adopted here applies to the setting where space is viewed as continuous but time is taken to be discrete. We view the data as a time series of spatial processes and work in the setting of dynamic models, achieving a class of dynamic models for such data. We seek rich, flexible, easy‐to‐specify, easy‐to‐interpret, computationally tractable specifications which allow very general mean structures and also non‐stationary association structures. Our modelling contributions are as follows. In the case where univariate data are collected at the spatial locations, we propose the use of a spatiotemporally varying coefficient form. In the case where multivariate data are collected at the locations, we need to capture associations among measurements at a given location and time as well as dependence across space and time. We propose the use of suitable multivariate spatial process models developed through coregionalization. We adopt a Bayesian inference framework. The resulting posterior and predictive inference enables summaries in the form of tables and maps, which help to reveal the nature of the spatiotemporal behaviour as well as the associated uncertainty. We illuminate various computational issues and then apply our models to the analysis of climate data obtained from the National Center for Atmospheric Research to analyze precipitation and temperature measurements obtained in Colorado in 1997. Copyright © 2005 John Wiley & Sons, Ltd.