A Low-Rank Bayesian Approach for Geoadditive Modeling

Kriging is an established methodology for predicting spatial data in geostatistics. Current kriging techniques can handle linear dependencies on spatially referenced covariates. Although splines have shown promise in capturing nonlinear dependencies of covariates, their combination with kriging, especially in handling count data, remains underexplored. This paper proposes a novel Bayesian approach to the low-rank representation of geoadditive models, which integrates splines and kriging to account for both spatial correlations and nonlinear dependencies of covariates. The proposed method accommodates Gaussian and count data inherent in many geospatial datasets. Additionally, Laplace approximations to selected posterior distributions enhances computational efficiency, resulting in faster computation times compared to Markov chain Monte Carlo techniques commonly used for Bayesian inference. Method performance is assessed through a simulation study, demonstrating the effectiveness of the proposed approach. The methodology is applied to the analysis of heavy metal concentrations in the Meuse river and vulnerability to the coronavirus disease 2019 (COVID-19) in Belgium. Through this work, we provide a new flexible and computationally efficient framework for analyzing spatial data.