Geometric Foundations for Interval
نویسنده
چکیده
The need to reason with imprecise probabilities arises in a wealth of situations ranging from pooling of knowledge from multiple experts to abstraction-based probabilistic planning. Researchers have typically represented imprecise probabilities using intervals and have developed a wide array of diierent techniques to suit their particular requirements. In this paper we provide an analysis of some of the central issues in representing and reasoning with interval probabilities. We use the well-developed area of convex geometry as the underlying foundation for our analysis. In particular, we point out the ubiquity of the probability cross-product operator, a generalization of which is known in the convex geometry literature as the Minkowski operator. We provide a throrough analysis of some key properties of this operator relative to manipulation of sets of probability distributions. We demonstrate the application of our results to the problems of inference in interval Bayesian networks and projection of abstract probabilistic actions.
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تاریخ انتشار 1998