Improved posterior probability estimates from prior and conditional linear constraint systems

C. C. White (1986) presented a method for computing interval bounds on posterior probabilities when the priors and conditionals are described by linear constraint systems. It is shown that White´s method gives an exact description of the possible posteriors in the special case where conditionals are precise and uniformity positive. A simple method for extending this result to precise zero conditionals is developed. Then, a method for computing interval ends on the posteriors is presented for the case of imprecise conditionals. These bounds are tight for interval and bounds are at least as tight as, and often tighter than, those found by White, and require little additional computational effort