INLA-RF: A hybrid modeling strategy for spatio-temporal environmental data

Environmental processes often exhibit complex, non-linear patterns and discontinuities across space and time, posing significant challenges for traditional geostatistical modeling approaches. To overcome this weakness a hybrid modeling strategy can be proposed. This hybrid strategy combines the interpretability and principled uncertainty quantification of statistical models with the predictive flexibility of machine learning methods. Specifically, two novel algorithms, collectively named INLA-RF, iteratively couple a Bayesian spatio-temporal model—fitted via the INLA-SPDE approach—with Random Forest. The framework enables uncertainty propagation across modeling stages, an aspect often overlooked in existing hybrid approaches. Additionally, an effective stopping criterion based on Kullback-Leibler divergence is introduced. Predictive performance and uncertainty quantification of the INLA-RF algorithms are evaluated using two simulation studies and a real air pollution application. Overall, the results indicate that INLA-RF can improve spatio-temporal predictive accuracy while retaining interpretability and providing coherent uncertainty estimates.