Calculation of posterior bounds given convex sets of prior probability measures and likelihood functions

This article presents alternatives and improvements to Lavine's algorithm, currently the most popular method for calculation of posterior expectation bounds induced by sets of probability measures. First, methods from probabi listic logic and Walley's and White-Snow's algorithms are reviewed and comp ared to Lavine's algorithm. Second, the calculation of posterior bounds is reduced to a fractional programming problem. From the unifying perspective of fractional programming, Lavine's algorithm is derived from Dinkelbach's algorithm, and the White-Snow algorithm is shown to be similar to the Charn es-Cooper transformation. From this analysis, a novel algorithm for expecta tion bounds is derived. This algorithm provides a complete solution for the calculation of expectation bounds from priors and likelihood functions spe cified as convex sets of measures. This novel algorithm is then extended to handle the situation where several independent identically distributed mea surements are available. Examples are analyzed through a software package t hat performs robust inferences and that is publicly available.