Education

Geostatistics is often misunderstood as "classical statistics applied to geospatial data". To correct this unfortunate misunderstanding, the best we can do as a community is to list educational resources.

Learning resources

Books

Lectures

  • Júlio Hoffimann - Video lectures with the GeoStats.jl project.

  • Edward Isaaks - Video lectures on variography, Kriging and related concepts.

  • Jef Caers - Video lectures on two-point and multiple-point methods.

Workshops

  • CBMina 2021 [Portuguese] - GeoStats.jl at the Brazilian mining congress.

  • UFMG 2021 [Portuguese] - GeoStats.jl at the Federal University of Minas Gerais.

GaussianProcesses.jl

GaussianProcesses.jl - Gaussian process regression and Simple Kriging are essentially two names for the same concept. The derivation of Kriging estimators, however; does not require distributional assumptions. It is a beautiful coincidence that for multivariate Gaussian distributions, Simple Kriging gives the conditional expectation. Matheron and other important geostatisticians have generalized Gaussian processes to more general random fields with locally-varying mean and for situations where the mean is unknown. GeoStats.jl includes Gaussian processes as a special case as well as other more practical Kriging variants.

MLKernels.jl

MLKernels.jl - Spatial structure can be represented in many different forms: covariance, variogram, correlogram, etc. Variograms are more general than covariance kernels according to the intrinsic stationary property. This means that there are variogram models with no covariance counterpart. Furthermore, empirical variograms can be easily estimated from the data (in various directions) with an efficient procedure. GeoStats.jl treats variograms as first-class objects.

Interpolations.jl

Interpolations.jl - Kriging and spline interpolation have different purposes, yet these two methods are sometimes listed as competing alternatives. Kriging estimation is about minimizing variance (or estimation error), whereas spline interpolation is about deriving smooth estimators for computer visualization. Kriging is a generalization of splines in which one has the freedom to customize spatial structure based on data. Besides the estimate itself, Kriging also provides the variance map as a function of point patterns.

MLJ.jl

MLJ.jl - Traditional statistical learning relies on core assumptions that do not hold in geospatial settings (fixed support, i.i.d. samples, ...). Geostatistical learning has been introduced recently as an attempt to push the frontiers of statistical learning with geospatial data.