发表机构
Faculty of Environment, Science and Economy, University of Exeter（埃克塞特大学环境、科学与经济学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究建立统一数学框架关联克里金法与高斯过程，弥合地理统计学与机器学习的方法学鸿沟，为两领域方法转换及进展互通提供基础。
AI 中文摘要
空间建模与推断广泛存在于科学与工程的诸多领域，克里金法（Kriging）与高斯过程（GP）回归是两种广泛使用的预测模型。尽管二者基于相同的随机场理论，但常被孤立对待，术语、符号及实际实现的差异掩盖了它们的联系，这种分离主要源于它们分别在地理统计学与机器学习领域独立发展。为弥合这一方法学鸿沟，本研究建立了一个统一的数学框架，将两种范式关联起来，在该框架中详细阐述并对比了每种方法的基础假设与公式，既凸显了差异又明确了联系。这一视角为从业者提供了在地理统计学与机器学习间转换概念和方法的共同基础，尤其使任一领域的方法学进展更易被另一领域理解，包括高斯过程文献中不确定性量化的进展。
英文摘要
Spatial modelling and inference arise across many areas of science and engineering, with Kriging and Gaussian process (GP) regression serving as two widely used predictive models. Although grounded in the same random field theory, these approaches are often treated in isolation. As a result, their connection has been obscured by differences in terminology, notation, and practical implementation. This separation largely reflects their independent development within geostatistics and machine learning, respectively. To bridge this methodological divide, this work establishes a unified mathematical framework that connects the two paradigms. The underlying assumptions and formulations of each approach are detailed and compared within this framework. This comparison highlights their differences while clarifying the connections between them. The resulting perspective provides practitioners with a common foundation for translating concepts and methods between geostatistics and machine learning. In particular, it makes methodological developments in either field more accessible to the other, including advances in uncertainty quantification from the GP literature.
