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Abstract:
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The prequential approach to statistics, originated by A. P. Dawid, puts the problem of making and testing statistical forecasts at the center of statistical theory and practice. The prequential principle requires that any criterion of agreement between the forecasts and actual outcomes should depend only on the actual observed sequences of forecasts and outcomes, and not further on the strategies (if any) which might have produced these. In has been realized in the early 1990s that a clean implementation of the prequential approach requires its own concept of probability, different from standard measure-theoretic probability. In this talk I will review game-theoretic probability, which is part of a tradition as old as measure-theoretic but which was formalized only recently. As opposed to measure-theoretic probability, game-theoretic probability fully respects the prequential principle.
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