Information geometry and Bayesian inference for high-dimensional parametric and semi-parametric models

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Prediction and inference methods for high-dimensional models and semiparametric models have been investigated. It is shown that the model manifold of the Neyman-Scott model is the space with constant negative curvature. The Neyman-Scott model is formulated as a transformation group model. A predictive density dominating the best invariant predictive density has been constructed by using information geometry. Furthermore, empirical likelihood methods for semiparametric models have been studied. Empirical likelihood methods were formulated in the framework of information geometry.Prediction methods for statistical problems with multiplicity have also been studied.