Kriging and variogram models
Geostatistics is a popular class of statistical methods for estimating, or predicting, the value of a continuous spatial process at unobserved locations given the value of the process at a set of known locations. Spatial prediction of this sort is typically performed using the method known as kriging, which provides estimates that are optimized over the class of predictors that are a linear combination of the observed values of the process. Beyond providing point estimates of the process at unobserved locations, the variances of kriging estimates (or kriging standard errors) are readily available as measures of uncertainty in predictions. An underlying assumption in kriging is that the covariance structure of the spatial process is known. Thus, before kriging can be performed, the spatial-dependence structure must be determined using the observed values of the process. Rather than estimating the covariance function of the spatial process directly, an alternative description of the spatial-dependence structure known as the variogram is estimated from the observed data. In this article, we review both kriging and variogram methods. In addition, we illustrate these methods using a rainfall dataset and provide brief introductions to some extensions of standard geostatistical methods.