I will discuss recent joint work with Haosui Duanmu and Daniel M. Roy, in which we give a precise characterization of admissibility in Bayesian terms, solving a long-standing problem in the field of statistical decision theory. This result uses so-called hyperpriors, which can give infinitesimal weight to events, to achieve this characterization, and also has interesting classical consequences (that is, not mentioning hyperpriors or infinitesimals). (I have already presented an early, weaker version of the present result in a previous lecture at the seminar; said result only held in problems with strictly convex loss functions. The present result holds without any assumptions on the loss function or the decision problem.)