The Art of Cross Validation in Geostatistical Applications

Geostatistical methods of estimating ore reserves and other spatial phenomena are becoming increasingly wide spread in their use. Properly applied, Geostatistical estimation falls into two stages -- the "modelling" of the spatial variability within the study area; and the use of this spatial model to provide an appropriate estimation technique. The first stage usually consists of construction and interpretation of semi-variogram graphs, and the second is the development of the corresponding Kriging method. Because of the apparent subjectivity inherent to the first stage of a geostatistical analysis, attempts have been made to provide methods of "testing' whether a particular semi-variogram model (say) adequately represents the study area. Increasingly, the choice of model is being justified by a process known as "Cross Validation'. With this approach, the analyst uses a partial data set to estimate values at actual sampled positions. "Real" and "estimated" values are then compared in such a way that the model can be accepted or rejected. This paper discusses the process of cross validation in some detail, using case studies as examples. Some problems with the technique are illustrated and discussed.