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

Fabio Gagliardi Cozman
Journal of Computational and Graphical Statistics
Vol. 8, No. 4 (Dec., 1999), pp. 824-838
DOI: 10.2307/1390829
Stable URL: http://www.jstor.org/stable/1390829
Page Count: 15
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Calculation of Posterior Bounds Given Convex Sets of Prior Probability Measures and Likelihood Functions
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Abstract

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 Charnes-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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