Cross-covariance functions for additive and coupled joint spatiotemporal SPDE models in R-INLA

Abstract

Models for multivariate space–time geostatistical data have received a growing interest in spatial and spatiotemporal epidemiology. However, specifying models that can capture associations within and among multivariate measurements is usually a challenge. The main goal of this paper is to introduce and review cross-covariance functions that are rich in structure and are computationally feasible. Integrated nested Laplace approximation combined with stochastic partial differential equations were used for inference and prediction, as a fast and precise alternative to the computationally intensive Markov chain Monte Carlo methods. A large set of models is considered in this paper: models assuming independent, shared or correlated spatial and temporal processes (with nine possible combinations), and models with independent, shared and linear models of coregionalization spatiotemporal processes. Different processes are applied to Culicoides data and compared. Bayesian spatial prediction results show that the central and Northeastern parts of Belgium had the highest prevalence of Culicoides in summer months and the lowest prevalence in winter months.