KRIGING AND SPLINES - AN EMPIRICAL-COMPARISON OF THEIR PREDICTIVE PERFORMANCE IN SOME APPLICATIONS

In disciplines such as soil science, ecology, meteorology, water resou rces, mining engineering, and forestry, spatial prediction is of centr al interest. A sparsely sampled spatial process yields imperfect knowl edge of a resource, from which prediction of unobserved parts of the p rocess are to be made. A popular stochastic method that solves this pr oblem is kriging. But the appropriateness of kriging-and, for that mat ter, of any method based on probabilistic models for spatial data-has been frequently questioned. A number of nonstochastic methods have als o been proposed, the leading contender of which appears to be splines. There has been some debate as to which of kriging and splines is bett er-a debate that has centered largely on operational issues, because t he two methods are based on different models for the process. In this article the debate is turned to where it ultimately matters-namely, th e precision of prediction based on real data. By dividing data sets in to modeling sets and prediction sets, the two methods may be compared. In the cases examined, kriging sometimes outperforms splines by a con siderable margin, and it never performs worse than splines. Various co nfigurations of data show that the sampling regime determines when kri ging will outperform splines.