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.
No takes yet. Share an insight, caveat, or question.
Diaconis et al. (1986) studied this question.
Synapse has enriched one closely related paper. Consider it for comparative context: