In disciplines such as soil science, ecology, meteorology, water resources, mining engineering, and forestry, spatial prediction is of central interest. A sparsely sampled spatial process yields imperfect knowledge of a resource, from which prediction of unobserved parts of the process are to be made. A popular stochastic method that solves this problem is kriging. But the appropriateness of kriging—and, for that matter, of any method based on probabilistic models for spatial data—has been frequently questioned. A number of nonstochastic methods have also been proposed, the leading contender of which appears to be splines. There has been some debate as to which of kriging and splines is better—a debate that has centered largely on operational issues, because the two methods are based on different models for the process. In this article the debate is turned to where it ultimately matters—namely, the precision of prediction based on real data. By dividing data sets into modeling sets and prediction...