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Spatial prediction in an arbitrary location, based on a spatial set ofobservations, is usually performed by Kriging, being the best linear unbiasedpredictor (BLUP) in a least-square sense. In order to predict a continuoussurface over a spatial domain a grid representation is most often used. Krigingpredictions and prediction variances are computed in the nodes of a gridcovering the spatial domain, and the continuous surface is assessed from thisgrid representation. A precise representation usually requires the number ofgrid nodes to be considerably larger than the number of observations. For aGaussian random field model the Kriging predictor coinsides with theconditional expectation of the spatial variable given the observation set. Analternative expression for this conditional expectation provides a spatialpredictor on functional form which does not rely on a spatial griddiscretization. This functional predictor, called the Kernel predictor, isidentical to the asymptotic grid infill limit of the Kriging-based gridrepresentation, and the computational demand is primarily dependent on thenumber of observations - not the dimension of the spatial reference domain norany grid discretization. We explore the potential of this Kernel predictor withassociated prediction variances. The predictor is valid for Gaussian randomfields with any eligible spatial correlation function, and large computationalsavings can be obtained by using a finite-range spatial correlation function.For studies with a huge set of observations, localized predictors must be used,and the computational advantage relative to Kriging predictors can be verylarge. Moreover, model parameter inference based on a huge observation set canbe efficiently made. The methodology is demonstrated in a couple of examples.

The Spatial Kernel Predictor based on Huge Observation Sets