Calculation of Posterior Bounds Given Convex Sets of Prior Probability Measures and Likelihood Functions

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.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 probabilistic logic and Walley's and White-Snow's algorithms are reviewed and compared 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 Chames-Cooper transformation. From this analysis, a novel algorithm for expectation bounds is derived. This algorithm provides a complete solution for the calculation of expectation bounds from priors and likelihood functions specified as convex sets of measures. This novel algorithm is then extended to handle the situation where several independent identically distributed measurements are available. Examples are analyzed through a software package that performs robust inferences and that is publicly available.

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