  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.
