IMPROVED POSTERIOR PROBABILITY ESTIMATES FROM PRIOR AND CONDITIONAL LINEAR CONSTRAINT SYSTEMS

White has presented a method for computing interval bounds on posterior probabilities when the priors and conditionals are described by linear constraint systems. It is now shown that White's method gives an exact description of the possible posteriors in the special case where conditionals are precise and uniformly positive. A simple method for extending this result to precise zero conditionals is developed. Then, a new method for computing interval bounds on the posteriors is presented for the case of imprecise conditionals. The new bounds are tight for interval and point conditionals. For general conditionals, the posterior bounds are at least as tight as, and often tighter than, those found by White, and require little additional computational effort.