Construction methods for predictive distributions under multiplicity

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It has been proved that priors maximizing the mutual information between the parameter and the quantity to be predicted given the observation play an essential role. By using this fact, prediction problems with multiplicity have been studied. It has been shown that predictive distributions resolving the multiplicity can be constructed as Bayesian predicitive distributions. The best prior distributions become complex and diffcult to obtain. Numerical approximation methods have been developed. In addition to binomial and multinomial models, prediction problems concerning linear regression models, time series models, and Wishart models have been investigated. Information geometrical properties of these models have been studied and applied to construct superior prediction.