SFU Computational Math Seminar - Hong Qian

Abstract: How to apply the mathematical theory of probability to real world problems? Interpretations of "what is probability" have led to the Bayesian and frequentist schools. In very elementary terms, I try to show how Gibbs' theory stitches together both thoughts, as well as the large deviations theory, an 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". Two well-known entropy functions, Gibbs' and Shannon's, figure prominently in our theory.