Statistics, Department of


Date of this Version



2012 International Society for Bayesian Analysis


Bayesian Analysis (2012) 7, Number 1, pp. 37{44


This paper makes a landmark contribution in three senses.

First, it provides many results that are fundamentally important in their own right. I refer specifically to Theorems 3 and 8. Theorem 3 treats arbitrary loss functions by breaking the integral into two terms, one It, where a difference of losses is bounded and another, IIt, where a bound on the moments of a difference of losses must be used. (All notation here is the same as the author's unless noted otherwise.) The treatment of these two terms reveals the role of the relative entropy and how the tails of the loss affect the risk, respectively. This is a proof that makes us wiser.