INLA-RF: A Hybrid Modeling Strategy for Spatio-Temporal Environmental Data

TL;DR

This paper introduces INLA-RF, a hybrid spatio-temporal modeling framework combining Bayesian INLA-SPDE and Random Forests to improve environmental data prediction and uncertainty quantification.

Contribution

The paper presents two novel algorithms, INLA-RF1 and INLA-RF2, integrating Bayesian models with RF in an iterative framework for better prediction and uncertainty propagation.

Findings

Hybrid approach improves spatio-temporal prediction accuracy.

Uncertainty quantification is coherent and effectively propagated.

Algorithms outperform traditional models in simulation studies.

Abstract

Environmental processes often exhibit complex, non-linear patterns and discontinuities across space and time, posing significant challenges for traditional geostatistical modeling approaches. In this paper, we propose a hybrid spatio-temporal modeling framework that combines the interpretability and uncertainty quantification of Bayesian models -- estimated using the INLA-SPDE approach -- with the predictive power and flexibility of Random Forest (RF). Specifically, we introduce two novel algorithms, collectively named INLA-RF, which integrate a statistical spatio-temporal model with RF in an iterative two-stage framework. The first algorithm (INLA-RF1) incorporates RF predictions as an offset in the INLA-SPDE model, while the second (INLA-RF2) uses RF to directly correct selected latent field nodes. Both hybrid strategies enable uncertainty propagation between modeling stages, an aspect often overlooked in existing hybrid approaches. In addition, we propose a Kullback-Leibler divergence-based stopping criterion. We evaluate the predictive performance and uncertainty quantification capabilities of the proposed algorithms through two simulation studies. Results suggest that our hybrid approach enhances spatio-temporal prediction while maintaining interpretability and coherence in uncertainty estimates.