Construction methods for predictive distributions under multiplicity

事实证明，在给定观测值的情况下，使参数与待预测量之间的互信息最大化的先验是至关重要的。利用这一事实，研究了具有多重性的预测问题。研究表明，解决多重性的预测分布可以构造为贝叶斯预测分布。最佳先验分布变得复杂且难以获得。数值近似方法已经发展起来。除了二项和多项模型外，还研究了线性回归模型、时间序列模型和Wishart模型的预测问题。研究了这些模型的信息几何特性，并将其应用于构建更优的预测。

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.