Geometric Foundations for IntervalBased Probabilities
Vu Ha and Peter Haddawy Decision Systems and Artificial Intelligence Lab Dept. of EE&CS University of WisconsinMilwaukee Milwaukee, WI 53201
The need to reason with imprecise probabil ities arises in a wealth of situations rang ing from pooling of knowledge from multi ple experts to abstractionbased probabilistic planning. Researchers have typically repre sented imprecise probabilities using intervals and have developed a wide array of differ ent techniques to suit their particular require ments. In this paper we provide an analysis of some of the central issues in representing and reasoning with interval probabilities. At the focus of our analysis is the probability crossproduct operator and its interval gen eralization, the ccoperator. We perform an extensive study of these operators relative to manipulation of sets of probability distribut tions. This study provides insight into the sources of the strengths and weaknesses of various approaches to handling probability intervals. We demonstrate the application of our results to the problems of inference in in terval Bayesian networks and projection and evaluation of abstract probabilistic plans.