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Institut für Wasser- und Umweltsystemmodellierung - IWS



"Measures of Parameter Uncertainty in Geostatistical Estimation"

Within applied and theoretical studies of site exploration and data assimilation or geostatistical inversion, measures of parameter uncertainty are required in order to assess the optimality of a suggested scheme. This study reviews and discusses measures for parameter uncertainty associated with so-called alphabetic criteria from the field of optimal design applied to geostatistical estimation. Further, there are several rather intuitive measures commonly applied in the literature and some new measures are suggested in this study. It is shown how these measures relate to the optimality alphabet and to the concept of relative entropy. Issues of physical and statistical significance are addressed if they arise. Also, computational feasibility is discussed and efficient ways to evaluate these measures are presented. A major conclusion is that the mean estimation variance and the averaged conditional integral scale are a powerful duo for characterizing conditional p arameter uncertainty with direct correspondence to the well-understood optimality alphabet. As most general representative of linear or linearized spatial estimation within the Bayesian framework, this study is based on cokriging generalized to uncertain mean and trends. Generalization to kriging and quasi-linear schemes is straightforward.