Bayesian logistic betting strategy against probability forecasting

TL;DR

This paper introduces a Bayesian logistic regression betting strategy for probability forecasting, demonstrating its effectiveness in outperforming forecasts by exploiting tendencies in the Japan Meteorological Agency's predictions.

Contribution

The paper develops a novel Bayesian logistic betting strategy within the game-theoretic probability framework and proves strong law of large numbers results for it.

Findings

Strategy outperforms the Japan Meteorological Agency's forecasts

Exploits the agency's avoidance of clear-cut predictions

Proves strong law of large numbers in the probability forecasting game

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.