The Annals of Statistics

On the Consistency of Bayes Estimates

Persi Diaconis and David Freedman

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Abstract

We discuss frequency properties of Bayes rules, paying special attention to consistency. Some new and fairly natural counterexamples are given, involving nonparametric estimates of location. Even the Dirichlet prior can lead to inconsistent estimates if used too aggressively. Finally, we discuss reasons for Bayesians to be interested in frequency properties of Bayes rules. As a part of the discussion we give a subjective equivalent to consistency and compute the derivative of the map taking priors to posteriors.

Article information

Source
Ann. Statist., Volume 14, Number 1 (1986), 1-26.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349830

Digital Object Identifier
doi:10.1214/aos/1176349830

Mathematical Reviews number (MathSciNet)
MR829555

Zentralblatt MATH identifier
0595.62022

JSTOR
links.jstor.org

Subjects
Primary: 62A15
Secondary: 62E20: Asymptotic distribution theory

Keywords
Consistency location problem Dirichlet prior merging of opinions foundations uniformities

Citation

Diaconis, Persi; Freedman, David. On the Consistency of Bayes Estimates. Ann. Statist. 14 (1986), no. 1, 1--26. doi:10.1214/aos/1176349830. https://projecteuclid.org/euclid.aos/1176349830


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