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The canonical technique for nonlinear modeling of spatial/point-referenceddata is known as kriging in geostatistics, and as Gaussian Process (GP)regression for surrogate modeling and statistical learning. This articlereviews many similarities shared between kriging and GPs, but also highlightssome important differences. One is that GPs impose a process that can be usedto automate kernel/variogram inference, thus removing the human from the loop.The GP framework also suggests a probabilistically valid means of scaling tohandle a large corpus of training data, i.e., an alternative to so-calledordinary kriging. Finally, recent GP implementations are tailored to make themost of modern computing architectures such as multi-core workstations andmulti-node supercomputers. We argue that such distinctions are important evenin classically geostatistical settings. To back that up, we presentout-of-sample validation exercises using two, real, large-scale borehole datasets involved in the mining of gold and other minerals. We pit classic krigingagainst the modern GPs in several variations and conclude that the latter canmore economical (fewer human and compute resources), more accurate and offerbetter uncertainty quantification. We go on to show how the fully generativemodeling apparatus provided by GPs can gracefully accommodate left-censoring ofsmall measurements, as commonly occurs in mining data and other boreholeassays.

Traditional kriging versus modern Gaussian processes for large-scale mining data