HIROSE YOSHIHIRO    Department   Undergraduate School  , School of Interdisciplinary Mathematical Sciences    Position   Associate Professor
Research Period	2014/04～2018/03
Research Topic	Prediction and Conditional Normalized Maximum Likelihood Distribution
Research Type	KAKENHI Research
Consignor	Japan Society for the Promotion of Science
Research Program Type	Grant-in-Aid for Young Scientists (B)
KAKENHI Grant No.	26730014
Representative Person	HIROSE Yoshihiro
Details	This research project treated the conditional normalized maximum likelihood distribution, which is a conditional probability distribution. We were also interested in a measure of probability distributions which is called the conditional regret. When we fix past observations and when we consider the average of the past observations, another probability distribution is superior to the conditional normalized maximum likelihood distribution if they are evaluated with the Kullback-Leibler information. That probability distribution attains the minimax of another measure of probability distributions, which is called the conditional regret risk. Furthermore, the probability distribution coincides with the projection of the conditional normalized maximum likelihood distribution on the space of the Bayesian predictions.