Expanding the regression analysis through the innovative applications of Bayesian methods

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The assumption of a prior information for a parameter contained in the sampling density is essential, and the use of a proper prior density is obviously desired. This view allows us to pursue fundamental subjects such as the smoothing method. I began with exploring the deviance information criterion (DIC). Our tools for this challenging problem are the use of the e-mixture predictor and the two notions of the unbiasedness of a potential function. Then I attempted to explore a cross-validation criterion (CVC). The induced CVC fortunately shows good performance, and the reasons of performance becomes clear. The results are expected to stimulate our future studies of this subject.