Parameter Uncertainty in Spatial Prediction: Checking its Importance by Cross-Validating the Wolfcamp and Rongelap Data Sets

Abstract

Traditional geostatistical prediction techniques assume that the covariance structure of the data is known. In practice, the covariance must be estimated from data, and the estimate is used for computing predictions. The additional parameter uncertainty about the covariance structure is therefore not properly taken into account by customary plug-in kriging methods. Bayesian (Kitanidis, 1986; Handcock and Stein, 1993) and model-based kriging (Diggle et al., 1998) naturally incorporate parameter uncertainty into the predictions. In this study, we compare model-based and plug-in kriging methods, using two sets of data: the pressure head of the Wolfcamp aquifer and the ¹⁷³caesium concentration in the ground of Rongelap Island. We used the precision of the predictions and the success in modelling the prediction uncertainty as criteria to rank the methods. The main results were: (i) plug-in kriging methods were as precise as model-based kriging, (ii) linear kriging successfully modelled prediction uncertainty, provided the marginal distribution was close to normal and the variogram was unbiasedly estimated for non-stationary data, (iii) model-based kriging failed to model the ¹³⁷Cs concentration accurately. Given these results and our experiences from an empirical comparison of non-linear kriging methods (Moyeed and Papritz, 2000; Papritz and Moyeed, 1999), we would suggest that the question of parameter uncertainty be looked into more closely.