Statistical decision theory takes inspiration from game theory to provide a basic framework in which one can reason about optimality (or lack thereof) of statistical methods, such as estimators and tests.

One (very weak) property of such methods is admissibility - roughly, a method of estimation is admissible if there is no other which does better under all circumstances (in a sense specified by the decision theoretical framework).

Although a weak property, admissibility is notoriously hard to characterize. Recently we have found a characterization of admissibility (in a large class of statistical problems) in Bayesian terms, by using prior probability distributions which can take on infinitesimal values.

(The talk will not presuppose any knowledge on statistics or nonstandard analysis. Joint work with D. Roy and H. Duanmu.)

https://zoom.us/meeting/register/tJUvcO2tqTMqEtdESHljnD_Ee4rneqRCkDqo

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