Geostatistics for Large Datasets on Riemannian Manifolds: A Matrix-Free Approach

Journal of Data Science

article

Mike Pereira¹  Nicolas Desassis²  Denis Allard³ 

[1] Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg;PSL University, Centre for geosciences and geoengineering;Biostatistics and Spatial Processes

关键词: anisotropy;    finite elements;    Gaussian process;    Laplace-Beltrami operator;    nonstationarity;   

DOI  :  10.6339/22-JDS1075

学科分类：土木及结构工程学

来源: JDS

【 摘 要 】

Large or very large spatial (and spatio-temporal) datasets have become common place in many environmental and climate studies. These data are often collected in non-Euclidean spaces (such as the planet Earth) and they often present nonstationary anisotropies. This paper proposes a generic approach to model Gaussian Random Fields (GRFs) on compact Riemannian manifolds that bridges the gap between existing works on nonstationary GRFs and random fields on manifolds. This approach can be applied to any smooth compact manifolds, and in particular to any compact surface. By defining a Riemannian metric that accounts for the preferential directions of correlation, our approach yields an interpretation of the nonstationary geometric anisotropies as resulting from local deformations of the domain. We provide scalable algorithms for the estimation of the parameters and for optimal prediction by kriging and simulation able to tackle very large grids. Stationary and nonstationary illustrations are provided.

【 授权许可】

CC BY