Probability distributions with given multivariate marginals and given dependence structure
Journal of Multivariate Analysis
Journal of Multivariate Analysis
Correlations and Copulas for Decision and Risk Analysis
Management Science
Assessing Dependence: Some Experimental Results
Management Science
Testing the PEARL model in the Netherlands and Sweden
Environmental Modelling & Software
An appropriateness framework for the Dutch Meuse decision support system
Environmental Modelling & Software
Environmental Modelling & Software
Technical assessment and evaluation of environmental models and software: Letter to the Editor
Environmental Modelling & Software
Short communication: Ten guidelines for effective data visualization in scientific publications
Environmental Modelling & Software
Environmental Modelling & Software
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The uncertainty in the predictions of models for the behaviour of environmental systems is usually very large. In many cases the widths of the predictive probability distributions for outcomes of interest are significantly larger than the differences between the expected values of the outcomes across different policy alternatives. This seems to lead to a serious problem for model-based decision support because policy actions appear to have an insignificant effect on variables describing their consequences, relative to the predictive uncertainty. However, in some cases it is evident that some of the alternatives at least lead to changes in the desired direction. A formal analysis of this situation is made based on the dependence structure of the variables of interest across different policy alternatives. This analysis leads to the conclusion that the uncertainty in the difference of model predictions corresponding to different policies may be significantly smaller than the uncertainty in the predictions themselves. The knowledge about the uncertainty in this difference may be relevant information for the decision maker in addition to the information usually provided. The conceptual development is supplemented with a presentation of convenient methods for practical implementation. These are illustrated with a simple, didactical model for the effect of phosphorus discharge reduction alternatives on phosphorus loading to a lake.