The Annals of Statistics

Belief Function Representations of Statistical Evidence

Peter Walley

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Statist., Volume 15, Number 4 (1987), 1439-1465.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176350603

Digital Object Identifier
doi:10.1214/aos/1176350603

Mathematical Reviews number (MathSciNet)
MR913567

Zentralblatt MATH identifier
0645.62003

JSTOR
links.jstor.org

Subjects
Primary: 62A99: None of the above, but in this section
Secondary: 60A05: Axioms; other general questions

Keywords
Belief functions Dempster's rule Bayesian inference likelihood likelihood principle prior probabilities Bayes' rule upper and lower probabilities

Citation

Walley, Peter. Belief Function Representations of Statistical Evidence. Ann. Statist. 15 (1987), no. 4, 1439--1465. doi:10.1214/aos/1176350603. https://projecteuclid.org/euclid.aos/1176350603


Export citation