标题： INLA-RF：一种用于时空环境数据的混合建模策略 显示英文标题

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

摘要： 环境过程通常在空间和时间上表现出复杂的非线性模式和不连续性，这对传统的地统计建模方法构成了重大挑战。 在本文中，我们提出了一种混合时空建模框架，该框架结合了贝叶斯模型的可解释性和不确定性量化——使用INLA-SPDE方法进行估计——与随机森林（RF）的预测能力和灵活性。 具体而言，我们引入了两种新的算法，统称为INLA-RF，它们在一个迭代的两阶段框架中将统计时空模型与RF相结合。 第一个算法（INLA-RF1）将RF预测作为偏移量纳入INLA-SPDE模型，而第二个算法（INLA-RF2）则使用RF直接校正选定的潜在场节点。 这两种混合策略实现了建模阶段之间的不确定性传播，这是现有混合方法中常被忽视的一个方面。 此外，我们提出了一种基于Kullback-Leibler散度的停止准则。 我们通过两个模拟研究评估了所提出算法的预测性能和不确定性量化能力。 结果表明，我们的混合方法在保持可解释性和不确定性估计的一致性的同时，提高了时空预测效果。 显示英文摘要

摘要： 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.