Hong Qian, UW Applied Math

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How to apply the mathematical theory of probability to real world problems? Interpretations of "what is probability" have led to the standoff between Bayesian and frequentist schools. In this talk, I try to show how Gibbs' theory stitches together both thoughts, as well as the large deviations theory, the asymptotic analysis of the law of large numbers. This yields the statistical ensemble as a parametric family of probabilistic models that are specifically informed by the nature of "observables" with infinitely many observations. Two wellknown entropy functions, Gibbs' and Shannon's, as well as Pitman–Koopman–Darmois theorem, figure prominently in our theory.