The search for an organizing physical framework for statistics

Abstract

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.