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Experimental Mathematics Seminar

Game-Theoretic Foundations for Probability and Statistics 

Glenn Shafer, Rutgers Business School 

Location:  Hill 705
Date & time: Thursday, 14 February 2019 at 5:00PM - 6:00PM

Abstract:    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 Foundations for Probability and Finance. In this book's formulation, probability typically involves a perfect-information game with 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). 

In this talk I will review the game-theoretic foundation for probability as briefly as possible and then discuss its application to mathematical statistics. The usual formulation for mathematical statistics begins with the assumption that the statistician has only partial knowledge of the probability measure that describes a phenomenon. The corresponding game-theoretic move is to suppose that the statistician stands outside the perfect-information game, seeing only some of the moves or some of its consequences. 

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