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

TL;DR

This paper introduces a Bayesian framework for automatically selecting smoothing parameters in flexible spatiotemporal regression models, demonstrated through groundwater contamination case studies, improving stability over traditional methods.

Contribution

It presents a novel Bayesian approach for automatic smoothing parameter selection in spatiotemporal p-spline models, with efficient computation exploiting matrix sparsity.

Findings

The proposed method is more stable than GCV and AIC-based strategies.

Demonstrated effectiveness through simulations and groundwater contamination examples.

Achieves fully-automatic, data-driven flexible modeling.

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. A computationally efficient implementation, exploiting the sparsity of the arising design and penalty matrices, is proposed. The findings are illustrated using a simulation and two examples, all concerned with the modelling of contaminants in groundwater, which suggest that the proposed strategy is more stable that competing strategies based on the use of criteria such as GCV and AIC.