On the Consistency of Bayes Estimates
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.
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