Computing optimum Bayesian confidence interval with applications

Computing a Bayesian confidence interval-of an unknown parameter of a probability distribution is an important problem in the interface of applied statistics and computer science. When the functional form of the posterior probability distribution is known, confidence interval is computed by using 'equal-tail' method which is not always optimal. We present algorithms for computing optimum alpha-confidence interval when the distribution can be modeled by a polygon. We investigate the properties of optimum solutions and present an O(n log k) algorithm to compute alpha-confidence intervals, where n is the number of vertices in the polygon and k is its modality.