Everyone is welcome to attend the ML seminar of Glenn Schafer ( Rutgers Business School – Newark and New Brunswick)
Title: Game-Theoretic Statistics
Fermat and Pascal’s two different methods for solving the problem of division lead to two different mathematical foundations for probability theory: a measure-theoretic foundation that generalizes the method of counting cases used by Fermat, and a game-theoretic foundation that generalizes the method of backward recursion used by Pascal. The game-theoretic foundation has flourished in recent decades, as documented by my forthcoming book with Vovk, Game-Theoretic Probability and Finance. In this book’s formulation, probability typically involves three players, a player who offers betting rates (Forecaster), a player who tests the reliability of the forecaster by trying to multiply the capital he risks betting at these rates (Skeptic), and a player who decides the outcomes (Reality).
Game-theoretic statistics is less developed but appears to offer powerful and flexible resources for applications. One way of using the
game between Forecaster, Skeptic, and Reality in applications is to suppose there are multiple Forecasters, each making forecasts according to a given probability model. This makes the picture look like standard statistical modeling in the tradition of Karl Pearson and R. A. Fisher, but it is only one possibility. In this talk, based on Chapter 10 of Game-Theoretic Probability and Finance, I will explore some other possibilities, drawing on examples from least squares, survival analysis, and quantum computing.