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On the Consistency of Bayes Estimates

Persi Diaconis and David Freedman
The Annals of Statistics
Vol. 14, No. 1 (Mar., 1986), pp. 1-26
Stable URL: http://www.jstor.org/stable/2241255
Page Count: 26
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On the Consistency of Bayes Estimates
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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.

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