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Title: Predictions for the gamma distribution model and information geometry of Levy measures Authors:  Fumiyasu Komaki - The University of Tokyo (Japan) [presenting]
Abstract: Some properties of predictive densities for the Gamma distribution and the inverse Gaussian distribution models are discussed. The performance of predictive densities is evaluated by the Kullback-Leibler divergence. For the normal and Poisson models, the correspondence between prediction and parameter estimation has played an essential role in prediction theory. On the other hand, such a simple relationship does not hold for the Gamma model and the inverse Gaussian model, and estimation of the Levy measures of the corresponding subordinators plays a role corresponding to the parameter estimation in the normal model and the Poisson model. The relationship between prediction for the Gamma and inverse Gaussian models and information geometry of the space of Levy measures is also discussed.