Bayesian statistics based on shrinkage prior

2016 Fiscal Year Final Research Report

• Project/Area Number: 25330035
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: The University of Tokyo
• Principal Investigator: Maruyama Yuzo 東京大学, 空間情報科学研究センター, 准教授 (30304728)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: ベイズ統計学 / 統計的決定理論

Outline of Final Research Achievements

This work treats the problem of estimating the predictive density of a random vector when both the mean vector and the variance are unknown. We prove that the density of reference in this context is inadmissible under the Kullback-Leibler loss in a nonasymptotic framework. Our result holds even when the dimension of the vector is strictly lower than three, which is surprising compared to the known variance setting. Finally, we discuss the relationship between the prediction and the estimation problems.

Free Research Field

統計科学