Minimaxity under the half-Cauchy prior

Abstract

This is a follow-up paper of Polson and Scott (2012, Bayesian Analysis), which claimed that the half-Cauchy prior is a sensible default prior for a scale parameter in hierarchical models. For estimation of a p-variate normal mean under the quadratic loss, they demonstrated that the Bayes estimator with respect to the half-Cauchy prior seems to be minimax through numerical experiments. In this paper, we theoretically establish the minimaxity of the corresponding Bayes estimator using the interval arithmetric.

The title of this article is quite similar to that of our previous article on arXiv 2308.09339, in which we discussed some variants of the half-Cauchy prior. In this article, we focus on the half-Cauchy prior itself