Bayesian inference and decision theory under shrinkage priors

• Project/Area Number: 16K00040
• 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, 大学院総合文化研究科, 教授 (30304728)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2018: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 統計学 / ベイズ統計学 / 統計的決定理論 / ミニマクス性 / スタイン問題 / 許容性 / 予測分布 / ベイズ理論

Outline of Final Research Achievements

We have studied admissibility of generalized Bayes estimators of a multivariate normal mean vector, theta, in the presence of an unknown scale, sigma, under scaled squared error loss. we find classes of generalized Bayes estimators that are admissible within the class of equivariant estimators.

Academic Significance and Societal Importance of the Research Achievements

データの背後に確率的な構造を想定する統計的モデルはデータから有用な結論を導くために広く使われている手法である．その中でも正規分布モデルは最も基本的であり，まず最初に妥当性が検討される重要なモデルである．そのパラメータ推定（特に平均）は長い歴史があり，多くの理論的な蓄積がある．しかし，その問題設定の簡単さにも関わらず理論的解明が不十分な問題が残されていた．そのような問題に対して，縮小型事前分布のもとでのベイズ推定量が理論的良さを持つことを示した．

Research Products

• [Int'l Joint Research] Rutgers University(米国)
• [Journal Article] Harmonic Bayesian Prediction Under α -Divergence (2019)
  • Author(s): Yuzo Maruyama, Takeru Matsuda, Toshio Ohnishi
  • Journal Title: IEEE Transactions on Information Theory Volume: 65 Issue: 9 Pages: 5352-5366
  • DOI: 10.1109/tit.2019.2915245
  • NAID: 120007017124
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Admissible Bayes equivariant estimation of location vectors for spherically symmetric distributions with unknown scale (2019)
  • Author(s): Yuzo Maruyama and William E. Strawderman
  • Journal Title: Annals of Statistics Volume: 印刷中
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] Posterior consistency of g-prior for variable selection with a growing number of parameters (2018)
  • Author(s): Wang, M. and Maruyama, Y.
  • Journal Title: Journal of Statistical Planning and Inferenc Volume: 196 Pages: 19-29
  • DOI: 10.1016/j.jspi.2017.10.007
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A sharp boundary for SURE-based admissibility for the normal means problem under unknown scale (2017)
  • Author(s): Maruyama Yuzo、Strawderman William E.
  • Journal Title: Journal of Multivariate Analysis Volume: 162 Pages: 134-151
  • DOI: 10.1016/j.jmva.2017.09.002
  • Peer Reviewed / Open Access / Int'l Joint Research
• [Journal Article] A sharp boundary for SURE-based admissibility for the Normal means problem under unknown scale (2016)
  • Author(s): Yuzo Maruyama, William E. Strawderman
  • Journal Title: Arxiv Volume: arXiv:1609.03241 Pages: 1-28
  • Open Access / Int'l Joint Research / Acknowledgement Compliant
• [Journal Article] Harmonic Bayesian prediction under alpha-divergence (2016)
  • Author(s): Yuzo Maruyama, Toshio Ohnishi
  • Journal Title: Arxiv Volume: arXiv:1605.05899 Pages: 1-23
  • Open Access
• [Presentation] Ensemble minimaxity of James-Stein estimators (2019)
  • Author(s): Yuzo Maruyama
  • Organizer: the “New and Evolving Roles of Shrinkage in Large-Scale Prediction and Inference” workshop
  • Int'l Joint Research / Invited
• [Presentation] Ensemble minimaxity of James-Stein estimators (2019)
  • Author(s): Yuzo Maruyama
  • Organizer: Symposium in Memory of Charles Stein
  • Int'l Joint Research / Invited
• [Presentation] Harmonic Bayesian prediction under alpha-divergence (2017)
  • Author(s): Yuzo Maruyama
  • Organizer: The 1st International Conference on Econometrics and Statistics (EcoSta 2017)
  • Int'l Joint Research / Invited
• [Presentation] Equivariant Admissibility for the Normal Means Problem Under Unknown Scale (2017)
  • Author(s): Yuzo Maruyama
  • Organizer: The Third Annual Kliakhandler Conference: International Conference on Bayesian Inference in Statistics and Statistical Genetics
  • Int'l Joint Research / Invited
• [Presentation] Harmonic Bayesian prediction under alpha-divergence (2016)
  • Author(s): Yuzo Maruyama
  • Organizer: 9th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2016)
  • Place of Presentation: University of Seville, Spain
  • Year and Date: 2016-12-09
  • Int'l Joint Research / Invited
• [Presentation] Harmonic Bayesian prediction under alpha-divergence (2016)
  • Author(s): Yuzo Maruyama
  • Organizer: International Conference on Statistical Distributions and Applications (ICOSDA 2016)
  • Place of Presentation: Crowne Plaza, Niagara Falls, Canada
  • Year and Date: 2016-10-14
  • Int'l Joint Research / Invited
• [Remarks] My homepage
  • URL: https://yuzo-maruyama.github.io/
• [Remarks] Yuzo Maruyama webpage
  • URL: https://yuzo-maruyama.github.io/