On Cokriging, Neural Networks, and Spatial Blind Source Separation for Multivariate Spatial Prediction

TL;DR

Multivariate spatial prediction from irregularly sampled data is challenging due to cross-dependencies between variables. The paper proposes SBSS as a preprocessing step that decomposes $X(s)$ into independent latent fields $Z(s)$ via an unmixing matrix, enabling univariate Kriging of latent components and reconstruction of the original field. In extensive simulations and a real moss dataset, SBSS-Kriging performs on par with or better than Cokriging, while neural networks underperform relative to Kriging-based methods. The approach offers a practical reduction in covariance modelling complexity with clear applicability to geostatistical prediction problems.

Abstract

Multivariate measurements taken at irregularly sampled locations are a common form of data, for example in geochemical analysis of soil. In practical considerations predictions of these measurements at unobserved locations are of great interest. For standard multivariate spatial prediction methods it is mandatory to not only model spatial dependencies but also cross-dependencies which makes it a demanding task. Recently, a blind source separation approach for spatial data was suggested. When using this spatial blind source separation method prior the actual spatial prediction, modelling of spatial cross-dependencies is avoided, which in turn simplifies the spatial prediction task significantly. In this paper we investigate the use of spatial blind source separation as a pre-processing tool for spatial prediction and compare it with predictions from Cokriging and neural networks in an extensive simulation study as well as a geochemical dataset.