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Bayesian logistic betting strategy against probability forecasting

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.