Objective Bayes methods for non-regular statistical models

• Project/Area Number: 17K14233
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Hiroshima University
• Principal Investigator: Hashimoto Shintaro 広島大学, 先進理工系科学研究科(理), 准教授 (60772796)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000); Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: ベイズ統計学 / 統計数学 / 客観事前分布 / 非正則モデル / 高次漸近理論 / ベイズ統計 / ベイズ予測 / 情報理論 / ロバスト統計

Outline of Final Research Achievements

I studied the selection of objective priors in Bayesian statistics. In particular, I derived objective priors and studied these properties for non-regular models by using three approaches. As a related study, we studied the theory and methodology for robust Bayesian inference with my collaborators.

Academic Significance and Societal Importance of the Research Achievements

ベイズ統計学においては事前分布の選択が重要であり，理論的根拠を備えた事前分布の選択法はベイズ統計学の客観的な利用において必須である．特に，理想的な条件が成り立っていない非正則な状況は実際問題では自然であるが従来の統計理論が使えないため，事前分布の観点から新たな知見を与えたことは意義あることである．

Research Products

• [Journal Article] Reference priors via α-divergence for a certain non-regular model in the presence of a nuisance parameter (2021)
  • Author(s): Hashimoto Shintaro
  • Journal Title: Journal of Statistical Planning and Inference Volume: 213 Pages: 162-178
  • DOI: 10.1016/j.jspi.2020.11.007
  • Peer Reviewed / Open Access
• [Journal Article] Improvement of Bobrovsky-Mayor-Wolf-Zakai Bound (2021)
  • Author(s): Koike Ken-ichi、Hashimoto Shintaro
  • Journal Title: Entropy Volume: 23 Issue: 2 Pages: 161-161
  • DOI: 10.3390/e23020161
  • Peer Reviewed / Open Access
• [Journal Article] Predictive probability matching priors for a certain non-regular model (2021)
  • Author(s): Hashimoto Shintaro
  • Journal Title: Statistics & Probability Letters Volume: 174 Pages: 109096-109096
  • DOI: 10.1016/j.spl.2021.109096
  • Peer Reviewed
• [Journal Article] Robust Bayesian Regression with Synthetic Posterior Distributions (2020)
  • Author(s): Hashimoto Shintaro、Sugasawa Shonosuke
  • Journal Title: Entropy Volume: 22 Issue: 6 Pages: 661-661
  • DOI: 10.3390/e22060661
  • Peer Reviewed / Open Access
• [Journal Article] On Default Priors for Robust Bayesian Estimation with Divergences (2020)
  • Author(s): Nakagawa Tomoyuki、Hashimoto Shintaro
  • Journal Title: Entropy Volume: 23 Issue: 1 Pages: 29-29
  • DOI: 10.3390/e23010029
  • Peer Reviewed / Open Access
• [Journal Article] Bobrovsky-Mayor-Wolf-Zakaiの下界の改良 (2020)
  • Author(s): 小池健一，橋本真太郎
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2157 Pages: 31-38
  • Open Access
• [Journal Article] Objective priors for divergence-based robust estimation (2020)
  • Author(s): Tomoyuki Nakagawa and Shintaro Hashimoto
  • Journal Title: arXiv preprint Volume: -
• [Journal Article] Robust Bayesian Regression with Synthetic Posterior (2019)
  • Author(s): Shintaro Hashimoto and Shonosuke Sugasawa
  • Journal Title: arXiv preprint Volume: -
• [Journal Article] Moment matching priors for non-regular models (2019)
  • Author(s): Shintaro Hashimoto
  • Journal Title: Journal of Statistical Planning and Inference Volume: 203 Pages: 169-177
  • DOI: 10.1016/j.jspi.2019.03.009
  • Peer Reviewed
• [Journal Article] Robust Bayesian inference via gamma-divergence (2019)
  • Author(s): Tomoyuki Nakagawa and Shintaro Hashimoto
  • Journal Title: Communications in Statistics Theory and Methods Volume: online Issue: 2 Pages: 343-360
  • DOI: 10.1080/03610926.2018.1543765
  • Peer Reviewed
• [Journal Article] Objective priors via moment matching criterion for non-regular models (2018)
  • Author(s): Shintaro Hashimoto
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2091 Pages: 55-64
• [Journal Article] Robust estimation of skew-normal distribution with location and scale parameters via log-regularly varying functions (2017)
  • Author(s): Shintaro Hashimoto
  • Journal Title: International Journal of Statistics and Systems Volume: 12 Pages: 813-822
  • Peer Reviewed / Open Access
• [Journal Article] Comparison of two robust Bayes estimations using the divergence (2017)
  • Author(s): 中川智之，橋本真太郎
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2047 Pages: 55-66
  • Open Access
• [Journal Article] Robust estimation of location and scale parameters for skew-normal distribution using log-Pareto function (2017)
  • Author(s): 橋本真太郎
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 2047 Pages: 67-76
  • Open Access
• [Presentation] Robust Bayesian modeling with synthetic posterior (2020)
  • Author(s): 橋本真太郎
  • Organizer: 広島大学統計金曜セミナー
  • Invited
• [Presentation] Moment matching priors for non-regular models (2019)
  • Author(s): Shintaro Hashimoto
  • Organizer: EAC-ISBA 2019 conference
  • Int'l Joint Research / Invited
• [Presentation] Moment matching priors for non-regular cases (2019)
  • Author(s): Shintaro Hashimoto
  • Organizer: 2019年度統計関連学会連合大会
• [Presentation] 一般事後分布に基づくベイズ推論とその応用 (2019)
  • Author(s): Shintaro Hashimoto
  • Organizer: 日本数学会2019年度秋季総合分科会
  • Invited
• [Presentation] Robust Bayesian estimation based on gamma-divergence (2018)
  • Author(s): Shintaro Hashimoto
  • Organizer: 2018 ISBA World Meeting
  • Int'l Joint Research
• [Presentation] Robust Bayesian inference via weighted likelihood functions (2018)
  • Author(s): Shintaro Hashimoto
  • Organizer: York - Hiroshima Joint Symposium 2018``Statistical Penalisation Methods and Dimension Reduction Methods for Economic and Financial Analysis"
  • Int'l Joint Research / Invited
• [Presentation] Robust parameter estimation based on quasi-posterior distributions (2018)
  • Author(s): Shintaro Hashimoto
  • Organizer: RIMS共同研究（公開型）「高次元量子雑音の統計モデリング」
  • Invited
• [Presentation] 非正則な確率分布族に対するmoment matching priorについて (2018)
  • Author(s): 橋本真太郎
  • Organizer: RIMS共同研究による研究会"Statistical Inference and Modelling”
• [Presentation] Asymptotic properties and robustness for the Bayes estimator based on the divergence (2017)
  • Author(s): 橋本真太郎
  • Organizer: 2017年度統計関連学会連合大会
• [Presentation] Statistical inference in terms of Bayesian inverse problem (2017)
  • Author(s): Shintaro Hashimoto
  • Organizer: Workshop for young scholars Control and inverse problems on waves, oscillations and flows -Mathematical analysis and computational methods-
  • Invited
• [Presentation] ダイバージェンスに基づくベイズ推定量の漸近的性質とロバスト性について (2017)
  • Author(s): 橋本真太郎
  • Organizer: 統計サマーセミナー2017
• [Presentation] Robust Bayesian inference based on quasi-posterior distributions (2017)
  • Author(s): Shintaro Hashimoto
  • Organizer: Statistics seminar in Radiation Effects Research Foundation
  • Invited
• [Remarks] Shintaro Hashimoto's website
  • URL: https://home.hiroshima-u.ac.jp/hashisin/