The Annals of Statistics
- Ann. Statist.
- Volume 14, Number 1 (1986), 1-26.
On the Consistency of Bayes Estimates
Persi Diaconis and David Freedman
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
http://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. http://projecteuclid.org/euclid.aos/1176349830.
