A nearest‐neighbour Gaussian process spatial factor model for censored, multi‐depth geochemical data

TL;DR: In this article , the authors investigate the relationship between local environmental variables and the geochemical composition of the Earth in a region spanning over 26,000 km2 in the lower South Island of New Zealand.

Abstract: We investigate the relationships between local environmental variables and the geochemical composition of the Earth in a region spanning over 26,000 km2 in the lower South Island of New Zealand. Part of the Southland–South Otago geochemical baseline survey—a pilot study pre‐empting roll‐out across the country—the data comprise the measurements of 59 chemical trace elements, each at two depth prescriptions, at several hundred spatial sites. We demonstrate construction of a hierarchical spatial factor model that captures inter‐depth dependency; handles imputation of left‐censored readings in a statistically principled manner; and exploits sparse approximations to Gaussian processes to deliver inference. The voluminous results provide a novel impression of the underlying processes and are presented graphically via simple web‐based applications. These both confirm existing knowledge and provide a basis from which new research hypotheses in geochemistry might be formed.