Title: A Low-Rank Bayesian Approach for Geoadditive Modeling Show Chinese title

Title: 基于低秩贝叶斯方法的地理加性建模

Abstract: 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. Show Chinese abstract

Abstract: 克里金法是地质统计学中用于预测空间数据的一种成熟方法。当前的克里金技术能够处理与空间相关协变量的线性依赖关系。尽管样条函数在捕捉协变量的非线性依赖方面显示出潜力，但它们与克里金法的结合，特别是在处理计数数据时，仍未得到充分探索。本文提出了一种新的贝叶斯方法，用于地理加性模型的低秩表示，该方法整合了样条函数和克里金法，以同时考虑空间相关性和协变量的非线性依赖关系。所提出的方法能够适应许多地理空间数据集中固有的高斯分布和计数数据。此外，对选定后验分布的拉普拉斯近似提高了计算效率，与常用的马尔可夫链蒙特卡罗贝叶斯推断技术相比，计算时间更快。通过模拟研究评估了该方法的性能，证明了所提出方法的有效性。该方法被应用于分析马斯河中的重金属浓度以及比利时对冠状病毒病（COVID-19）的脆弱性。通过这项工作，我们提供了一个新的灵活且计算高效的分析空间数据的框架。