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Bayesian logistic betting strategy against probability forecasting

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  • Masayuki Kumon
  • Jing Li
  • Akimichi Takemura
  • Kei Takeuchi
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    Abstract

    We propose a betting strategy based on Bayesian logistic regression modeling for the probability forecasting game in the framework of game-theoretic probability by Shafer and Vovk (2001). We prove some results concerning the strong law of large numbers in the probability forecasting game with side information based on our strategy. We also apply our strategy for assessing the quality of probability forecasting by the Japan Meteorological Agency. We find that our strategy beats the agency by exploiting its tendency of avoiding clear-cut forecasts.

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    File URL: http://arxiv.org/pdf/1204.3496
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1204.3496.

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    Date of creation: Apr 2012
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    Publication status: Published in Stochastic Analysis and Applications 31 (2013) 214-234
    Handle: RePEc:arx:papers:1204.3496

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    Web page: http://arxiv.org/

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    1. Kei Takeuchi & Akimichi Takemura & Masayuki Kumon, 2009. "New procedures for testing whether stock price processes are martingales," Papers 0907.3273, arXiv.org, revised Feb 2010.
    2. Masayuki Kumon & Akimichi Takemura & Kei Takeuchi, 2005. "Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games," Papers math/0510662, arXiv.org, revised Sep 2008.
    3. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29.
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