Using additive and coupled spatiotemporal SPDE models: a flexible illustration for predicting occurrence of Culicoides species

- Care has to be taken for choosing an optimal mesh.
- Coupled spatiotemporal models have better prediction accuracy than additive models.
- Misspecifying the spatial and temporal models has little impact on prediction.
- The increase in number of locations slightly improves the prediction performance.
- The highest prevalence of Culicoides was found in the central Belgium during summer.

This paper formulates and compares a general class of spatiotemporal models for univariate space-time geostatistical data. The implementation of stochastic partial differential equation (SPDE) approach combined with integrated nested Laplace approximation into the R-INLA package makes it computationally feasible to use spatiotemporal models. However, the impact of specifying models with and without space-time interaction is unclear. We formulate an extensive class of additive and coupled spatiotemporal SPDE models and investigate the distinction between them by (1) Extending their temporal effect, allowing a random walk process in time, (2) varying the spatial correlation function and (3) running a simulation study to assess the effect of misspecifying the spatial and temporal models, and to assess the generalizability of our results to a higher number of locations. Our methods are illustrated with Culicoides data from Belgium. The Bayesian spatial predictions showed that the highest prevalence of Culicoides species was found in the Northeastern and central parts of Belgium during summer.