The search for an organizing physical framework for statistics
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Theories of statistical analysis remain in conflict and contradiction. But nature reveals an elegant and coherent formulation of statistics in the thermal properties of physical systems. Demanding that a viable statistical theory share the properties of a viable physical theory---observer independence and coordinate invariance---resolves outstanding controversies in statistical model selection. Furthermore, by using constructions taken directly from thermodynamics, a predictive approach to model selection can be reconciled with a Bayesian approach to parameter uncertainty. This approach also solves the longstanding problem of the undetermined Bayesian prior.
- Physics