An important problem in geostatistics is to build models of the subsurface of the Earth given physical measurements at sparse spatial locations.
From earth system sciences to climate modeling and ecology, many of the greatest empirical modeling challenges are geographic in nature.
We formally establish results on the identifiability and consistency of the nugget in spatial models based upon the Gaussian process within the framework of in-fill asymptotics, i. e. the sample size increases within a sampling domain that is bounded.
SPATIAL INTERPOLATION STATISTICS THEORY STATISTICS THEORY
We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process).