Decision making with imprecise probabilities: Dempster‐Shafer Theory and application

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Abstract
The information and data used to support decision making under uncertainty in water resources situations can often be characterized as being very limited or weak. The representation of knowledge in conventional Bayesian decision analysis is in the form of precisely specified distributions and is the same no matter how weak the information source for this knowledge. A Bayesian analysis therefore may inadvertently impart too much precision to the input information and to the results. The concept of imprecise probability addresses this problem of excessive precision and a number of methods incorporating this concept have emerged. One such method, developed by Dempster and Shafer, accommodates greater imprecision by allowing the specification of probabilities on intervals. Theoretical aspects of the Dempster‐Shafer methodology and its application to inference and decision analysis are described. A water resources example of an application of the Dempster‐Shafer approach is presented, and the results contrasted with those obtained from the closest equivalent Bayesian scheme.