Comparison of Three Methods of Spatial Prediction

Abstract

Three methods for spatial prediction in Gaussian and transformed Gaussian random fields are described and compared.The first two methods are ordinary kriging and trans-Gaussian kriging.The third method is the Bayesian Transformed Gaussian model (BTG), which provides an alternative to trans-Gaussian kriging by taking into account the uncertainty about the exact parameter in the 'normalizing transformation.'All three methods were applied to the simulated data sets for each of four correlation families (exponential, rational quadratic, spherical and Matern) and to actual rainfall intensity data sets. The normalizing transformation was selected from the family of Box-Cox transformations.Cross validation on the simulated data shows that all three methods are close in terms of the mean squared error (MSE) and that BTG provides more realistic prediction intervals. The analysis of the rainfall data in terms of cross-validation shows that kriging and BTG are comparable.