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December, 1987 Belief Function Representations of Statistical Evidence
Peter Walley
Ann. Statist. 15(4): 1439-1465 (December, 1987). DOI: 10.1214/aos/1176350603


In Glenn Shafer's theory of parametric statistical inference, observational evidence and prior evidence are separately represented by belief or commonality functions $Q$ and $R$, which are then combined by Dempster's rule. We characterise, for finite parameter spaces, the functionals $Q$ and $R$ for which statistically independent observations may be combined by Dempster's rule, and those for which Dempster's rule is consistent with Bayes' rule. The functionals are determined up to an arbitrary partition of the parameter space and an arbitrary scale parameter, which might be chosen to reflect aspects of the evidence on which the statistical model is based. Our results suggest that Dempster's rule is not generally suitable for combining evidence from independent observations nor for combining prior beliefs with observational evidence.


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Peter Walley. "Belief Function Representations of Statistical Evidence." Ann. Statist. 15 (4) 1439 - 1465, December, 1987.


Published: December, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0645.62003
MathSciNet: MR913567
Digital Object Identifier: 10.1214/aos/1176350603

Primary: 62A99
Secondary: 60A05

Rights: Copyright © 1987 Institute of Mathematical Statistics


Vol.15 • No. 4 • December, 1987
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