Unbiased Block Predictions and Exceedance Probabilities for Environmental Thresholds

ABSTRACT Decision makers will in an emergency situation often be interested in predictions of harmful environmental variables relative to a certain threshold. We are therefore examining the robustness of different methods which are supposed to give unbiased estimates relative to such a threshold, both for point predictions and areal averages. We are also interested in exceedance probabilities. The methods (ordinary kriging, the so-called IWQSEL-predictor and a modified ordinary kriging predictor) are tested on different simulated data sets with respect to different goodness-of-fit criteria. The results indicate that the last two methods are comparable, and both are considerably better than ordinary kriging for predicting these spatial extremes. We do also examine the possibility of using a different approach based on an alternative estimation of the kriging error for better characterizing the predictive distributions for non-stationary fields. The results indicate that this approach can have certain advantages.