Massimiliano Amarante – Université de Montréal, Canada
We will take off from the observation that Savage’s axioms (or any axiomatization of EU) map Statistics into (classical) probability theory. Consequently, the axioms of any non-Bayesian model must map Statistics into something else. This observation raises the question of which Statistical theories would emerge via this mapping. We show that many non-Bayesian models map Statistics into alternative theories of probability that display the same structure as classical probability and differ from the latter only in the notion of approximation they use. We then build a general framework encompassing all the models displaying this structure and use it to identify the rules of inference corresponding to several popular models. We conclude by discussing the implications of our findings for issues such dynamic consistency, updating of capacities as well as some open problems.
Campus de l'Université de Montréal
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