Geostatistics for Large Datasets on Riemannian Manifolds: A Matrix-Free Approach
Artikel i vetenskaplig tidskrift, 2022

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.

anisotropy

Laplace-Beltrami operator

Gaussian process

finite elements

nonstationarity

Författare

Mike Pereira

Chalmers, Elektroteknik, System- och reglerteknik

Mines ParisTech

Nicolas Desassis

Mines ParisTech

Denis Allard

Biostatistique et Processus Spatiaux (BioSP)

Journal of Data Science

1680-743X (ISSN) 1683-8602 (eISSN)

Vol. 20 4 512-532

Styrkeområden

Informations- och kommunikationsteknik

Ämneskategorier

Beräkningsmatematik

Sannolikhetsteori och statistik

Datorseende och robotik (autonoma system)

DOI

10.6339/22-JDS1075

Mer information

Senast uppdaterat

2024-05-21