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Explore the foundations of Neo-Bayesian Statistics in this 1-hour 7-minute DS4DM Coffee Talk presented by Massimiliano Amarante from Université de Montréal, Canada. Delve into the observation that Savage's axioms map Statistics into classical probability theory, and investigate how non-Bayesian models map Statistics into alternative theories. Discover a general framework encompassing models with similar structures to classical probability, differing only in their notion of approximation. Examine the rules of inference corresponding to popular models and discuss implications for dynamic consistency, updating of capacities, and open problems in the field.