Demystifying the connections between Gaussian Process Regression and Kriging

Gaussian Process (GP) regression is a flexible, non-parametric Bayesian approach towards regression prob-lems that has seen increasing adoption for machine learning (ML) applications. Despite its recent popularity within the ML community, GP regression has a long history in geostatistics, where it is better known as kriging and is commonly used for spatial interpolation. The rapid development of GP regression in ML pre-sents significant opportunities for advanced knowledge transfer to the geotechnical engineering community. However, this knowledge transfer has often been inhibited by the different terminology and conventions adopted in both fields. This obscures the underlying science and introduces much potential for confusion. Therefore, this paper aims to reveal the connections between GP regression and kriging theories, with a view of acting as a bridge to increase the uptake of the latest developments in each field.