Scalable modeling of nonstationary covariance functions with non-folding B-spline deformation

TL;DR

This paper introduces a scalable, non-folding B-spline based deformation method for nonstationary covariance modeling, enabling efficient analysis of large environmental datasets with constrained, bijective spatial deformations.

Contribution

It presents a novel low-rank B-spline deformation approach that ensures non-folding, bijective transformations, improving computational scalability and applicability to large spatial datasets.

Findings

Successfully applied to rainfall data in Brazil

Ensures non-folding, bijective deformations

Enables scalable analysis of large datasets

Abstract

We propose a method for nonstationary covariance function modeling, based on the spatial deformation method of Sampson and Guttorp [1992], but using a low-rank, scalable deformation function written as a linear combination of the tensor product of B-spline basis. This approach addresses two important weaknesses in current computational aspects. First, it allows one to constrain estimated 2D deformations to be non-folding (bijective) in 2D. This requirement of the model has, up to now,been addressed only by arbitrary levels of spatial smoothing. Second, basis functions with compact support enable the application to large datasets of spatial monitoring sites of environmental data. An application to rainfall data in southeastern Brazil illustrates the method