  The canonical technique for nonlinear modeling of spatial/point-referenced
data is known as kriging in geostatistics, and as Gaussian Process (GP)
regression for surrogate modeling and statistical learning. This article
reviews many similarities shared between kriging and GPs, but also highlights
some important differences. One is that GPs impose a process that can be used
to automate kernel/variogram inference, thus removing the human from the loop.
The GP framework also suggests a probabilistically valid means of scaling to
handle a large corpus of training data, i.e., an alternative to so-called
ordinary kriging. Finally, recent GP implementations are tailored to make the
most of modern computing architectures such as multi-core workstations and
multi-node supercomputers. We argue that such distinctions are important even
in classically geostatistical settings. To back that up, we present
out-of-sample validation exercises using two, real, large-scale borehole data
sets involved in the mining of gold and other minerals. We pit classic kriging
against the modern GPs in several variations and conclude that the latter can
more economical (fewer human and compute resources), more accurate and offer
better uncertainty quantification. We go on to show how the fully generative
modeling apparatus provided by GPs can gracefully accommodate left-censoring of
small measurements, as commonly occurs in mining data and other borehole
assays.
