Geostatistical Prediction: Kriging

Abstract

Kriging is the geostatistical method of prediction. It is a best linear unbiased predictor on punctual or block supports; best in the sense that its prediction error variances are minimized. It is in practice a weighted moving average in which the weights depend on the variogram and the configuration of the sample points within the neighbourhood of its targets. Ordinary kriging is by far the most popular method, partly because it is robust with respect to departures from the underlying assumptions. There are, however, numerous more advanced types of kriging for specific tasks. Examples illustrate the effects on the kriging weights, the predictions and the prediction variances of changing the variogram parameters and the sample configurations. Punctual and block kriging are compared for mapping the predictions and errors. Kriging in the presence of anisotropy, simple kriging and lognormal kriging are also illustrated. A solution for back-transformation to the original scale is given for lognormal kriging. Punctual kriging can be used to identify suitable variogram models from the diagnostic statistics of ‘leave-one-out’ cross-validation.