A reformulation of Bayesian statistics as pediction theory and its applications

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Constructing methods for prior distributions in Bayesian statistics based on maximization of the conditional mutual information are investigated. In particular, statistical testing problems are formulated as a prediction problem by setting the null hypothesis as 0 and the alternative hypothesis as 1. It is shown that prior distributions that have not been considered in previous studies naturally appear. Numerical algorithms for maximizing the mutual information are developed.