Speaker: Geoff Nicholls, Department of Statistics, University of Oxford
Title: The Savage Axioms for Dummies
Abstract: In Bayesian inference the subjective expected utility is an object of foundational importance. The decision maker’s choices maximise this utility, and so it decides some elements of our statistical methodology.
For the SEU to exist we need a prior and a utility representing the subjective beliefs of the analyst to exist.
The Savage Axioms are a set of axioms which impose a certain “consistency” on our beliefs and values, and are sufficient for a representative prior and utility function to exist. I will present the axioms in the form given by Maurice de Groot,and look at two famous paradoxes which show, or appear to show, that some very natural human beliefs and values are in conflict with these axioms.I will mention some approaches to resolving of these paradoxes and conclude with a brief evaluation of the axioms.