AI 中文总结
本文梳理五十年空间统计学从克里金法到Spatial AI的发展，阐述其核心方法、数据融合与不确定性量化等内容，提出二者可融合以支撑具科学意义的预测。
AI 中文摘要
空间统计学已从用于空间预测的克里金法发展为面向复杂相依数据学习的广泛框架。本文追溯其发展历程，从随机场与谱方法到贝叶斯层次模型及可扩展计算，再将这些基础与空间人工智能（Spatial AI）相联结，其中图学习与神经网络正被适配于空间相依数据。本文介绍克里金法与非平稳性的核心思想，说明数据融合与不确定性量化如何将空间推理扩展至更复杂场景。核心贡献是统一阐述这些发展如何自然催生新型空间人工智能。我们未将空间统计学与机器学习视为独立体系，而是展示二者如何在保留可解释结构的同时从相依性中学习，还探讨空间几何与物理知识如何指导灵活的表征学习，支撑具科学意义的预测。
英文摘要
Spatial statistics has grown from kriging for spatial prediction into a broad framework for learning from complex dependent data. This article traces that development from random fields and spectral methods to Bayesian hierarchical models and scalable computation. It then connects these foundations to Spatial AI, where graph learning and neural networks are being adapted to spatially dependent data. The article introduces the main ideas behind kriging and nonstationarity and explains how data fusion and uncertainty quantification extend spatial inference to more complex settings. The central contribution is a unified account of how these developments lead naturally to new forms of Spatial AI. Rather than treating spatial statistics and machine learning as separate traditions, we show how both learn from dependence while preserving interpretable structure. We also examine how spatial geometry and physical knowledge can guide flexible representation learning and support scientifically meaningful prediction.
Comments68 pages; invited review article on the development of spatial statistics from kriging and classical dependence modeling to modern Spatial AI
