Efficient and automatic methods for flexible regression on spatiotemporal data, with applications to groundwater monitoring

Abstract

Fitting statistical models to spatiotemporal data requires finding the right balance between imposing smoothness and following the data. In the context of P-splines, we propose a Bayesian framework for choosing the smoothing parameter, which allows the construction of fully automatic data-driven methods for fitting flexible models to spatiotemporal data. An implementation, which is highly computationally efficient and exploits the sparsity of the design and penalty matrices, is proposed. The findings are illustrated using a simulation study and two examples, all concerned with the modelling of contaminants in groundwater. This suggests that the proposed strategy is more stable that competing methods based on the use of criteria such as generalised cross-validation and Akaike's Information Criterion.