摘要
【意义】经典统计推断依赖大样本与独立同分布前提,但时空数据却往往不满足这两大前提,因此,经典统计框架下的时空统计方法具有一定理论局限;相较而言,贝叶斯统计范式下的时空统计方法通过融合先验信息、引入参数随机性,形成统一的概率推断框架,可考虑更多不确定性,并能有效克服时空数据中的小样本和非独立问题,在时空统计建模中体现出较强的自身优势,并受到广泛关注和快速发展。【进展】本文首先从方法论演进角度出发,从传统贝叶斯时空统计与贝叶斯时空机器学习两个视角系统梳理了主流的贝叶斯时空统计模型,前者包括贝叶斯时空演化层次模型、贝叶斯时空回归层次模型、贝叶斯空间面板数据模型、贝叶斯时空地理加权回归模型、贝叶斯时空变系数模型和贝叶斯网格化时空高斯过程模型,后者包括贝叶斯时空因果森林模型、贝叶斯时空神经网络模型和贝叶斯时空图卷积神经网络模型;后又从实际应用方面,重点回顾了贝叶斯时空统计模型在公共卫生、环境科学、经济社会与公共安全、能源与工程等领域的应用。【展望】贝叶斯时空统计方法需在多源异构数据建模、深度学习融合、因果推断机制引入及高性能计算优化等方面实现突破,以兼顾理论完备性与实践适应性,推动其发展为具备因果推断、自适应泛化及智能分析的下一代时空建模范式。
[Objectives]Classical statistical inference typically relies on the assumptions of large sample sizes and independent,identically distributed(i.i.d.)observations,conditions that spatio-temporal data frequently violate,leading to inherent theoretical limitations in conventional approaches.In contrast,Bayesian spatio-temporal statistical methods integrate prior knowledge and treat all model parameters as random variables,thereby forming a unified probabilistic inference framework.This enables the incorporation of a broader range of uncertainties and offers robustness in modelling small samples and dependent structures,making Bayesian methods highly advantageous and increasingly influential in spatio-temporal analysis.[Progress]From the perspective of methodological evolution,this paper systematically reviews mainstream Bayesian spatio-temporal statistical models from two complementary perspectives:traditional Bayesian statistics and the Bayesian machine learning.The former includes Bayesian Spatio-temporal Evolutionary Hierarchical Models,Bayesian Spatio-temporal Regression Hierarchical Models,Bayesian Spatial Panel Data Models,Bayesian Geographically Weighted Spatio-temporal Regression Models,Bayesian Spatio-temporal Varying Coefficient Models,and Bayesian Spatio-temporal Meshed Gaussian Process Model.The latter includes Bayesian Causal Forest Models,Bayesian Spatio-temporal Neural Networks,and Bayesian Graph Convolutional Neural Networks.In terms of application,the review highlights representative studies across domains such as public health,environmental sciences,socio-economic and public safety,as well as energy and engineering.[Prospect]Bayesian spatio-temporal statistical methods need to achieve breakthroughs in multi-source heterogeneous data modeling,integration with deep learning,incorporation of causal inference mechanisms,and optimization of high-performance computing.These advances are essential to balance theoretical rigor with practical adaptability and to promote the development of a next-generation spatio-temporal modeling paradigm characterized by causal inference,adaptive generalization,and intelligent analysis.
作者
李俊明
胡雅璇
王楠楠
王斯雅琦
王若兰
吕琳
房紫晴
LI Junming;HU Yaxuan;WANG Nannan;WANG Siyaqi;WANG Ruolan;LYU Lin;FANG Ziqing(School of Statistics,Shanxi University of Finance and Economics,Taiyuan 030006,China;Baotou Natural Resources Survey and Utilization Center,Inner Mongolia,Baotou 014010,China)
出处
《地球信息科学学报》
北大核心
2025年第7期1501-1519,共19页
Journal of Geo-information Science
基金
国家社科基金重大项目(24&ZD183)。
关键词
贝叶斯统计
时空统计
时空依赖建模
层次模型
机器学习
因果推断
Bayesian statistics
spatio-temporal statistics
spatio-temporal dependency modeling
hierarchical models
machine learning
causal inference
