A characterization of Bayesian robustness for a normal location parameter

摘要

We consider the Bayesian estimation of a location parameter θ based on one observation x from a univariate normal distribution with mean θ and variance one, together with a prior π. In general, the mean t(x) in the posterior distribution does not satisfy the requirement that x − t(x) vanishes as x approaches ∞ (for example, when π is normal or Laplace), that is, the prior is not robust. In this paper we obtain, under mild regularity conditions on π, a necessary and sufficient (and easy to apply) condition for robustness, and identify classes of robust priors. Special attention is paid to the Subbotin prior because of its role in Bayesian model averaging.