---
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 [@ShaVov01]. 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.'
author:
- 'Masayuki Kumon[^1], Jing Li[^2], Akimichi Takemura and Kei Takeuchi[^3]'
bibliography:
- 'logistic.bib'
date: April 2012
title: Bayesian logistic betting strategy against probability forecasting
---

[*Keywords and phrases:*]{}   exponential family, game-theoretic probability, Japan Meteorological Agency, probability of precipitation, strong law of large numbers.

Introduction {#sec:intro}
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In this paper we consider assessing quality of probability forecasting for binary outcomes. A primary example of probability forecasting is the probability of precipitation announced by weather forecasting agencies. The binary outcomes are either “rain” (more precisely, precipitation above certain amount during a specified period at a particular location) or “no rain”. In the United States the National Weather Service started to announce probability of precipitation in 1965 