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A new development in Bayesian model averaging from the viewpoints of thermodynamics

Research Project

Project/Area Number 26330044
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Statistical science
Research InstitutionKyushu University

Principal Investigator

Ohnishi Toshio  九州大学, 経済学研究院, 教授 (60353413)

Co-Investigator(Kenkyū-buntansha) Dunn Peter  University of the Sunshine Coast, Associate Professor
Co-Investigator(Renkei-kenkyūsha) YANAGIMOTO Takemi  統計数理研究所, 名誉教授 (40000195)
Project Period (FY) 2014-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords統計科学 / Bayesモデル平均 / Bayes予測問題 / 熱力学 / モデル平均 / Bayeモデル平均 / Bayes予測 / モデル選択
Outline of Final Research Achievements

We formulate a prediction problem, which is an estimation of a probability density, as a risk minimization problem. Here we adopt the alpha-divergence as a loss function for evaluating the goodness of a prediction. The alpha-divergence is a generalization of the Kullback-Leibler divergence. Through this minimization problem, we reveal a duality between the likelihood maximization and the Shannon entropy maximization, which are two of the most important principles in statistical science.

Report

(4 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (15 results)

All 2017 2016 2015 2014

All Journal Article (6 results) (of which Open Access: 5 results,  Peer Reviewed: 2 results,  Acknowledgement Compliant: 2 results) Presentation (9 results)

  • [Journal Article] α-ダイバージェンス損失の下でのStein現象2017

    • Author(s)
      大西俊郎
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
  • [Journal Article] Harmonic Bayesian prediction under alpha-divergence.2016

    • Author(s)
      Maruyama, Y. & Ohnishi, T.
    • Journal Title

      Arxiv

      Volume: 1605.05899 Pages: 1-23

    • Related Report
      2016 Annual Research Report
    • Open Access
  • [Journal Article] Toshio Ohnishi,Bayes予測における尤度最大化とShannon entropy最大化の双対性2015

    • Author(s)
      大西 俊郎
    • Journal Title

      日本統計学会誌

      Volume: 45 Pages: 119-141

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 変分的手法に基づく尤度およびentropyの拡張2015

    • Author(s)
      大西 俊郎
    • Journal Title

      京都大学 数理解析研究所 講究録

      Volume: 1954 Pages: 61-72

    • Related Report
      2015 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] Permissible boundary prior function as a virtually proper prior density2014

    • Author(s)
      Takemi Yanagimoto, Toshio Ohnishi
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: (Accepted) Issue: 4 Pages: 789-809

    • DOI

      10.1007/s10463-013-0421-1

    • NAID

      40020116671

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bayes予測における尤度とエントロピーの双対性2014

    • Author(s)
      大西俊郎
    • Journal Title

      京都大学 数理解析研究所 講究録

      Volume: 1910 Pages: 29-42

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Presentation] α-ダイバージェンス損失の下でのStein現象2017

    • Author(s)
      大西俊郎
    • Organizer
      RIMS共同研究による研究会 "Bayes Inference and Its Related Topics"
    • Place of Presentation
      京都大学数理解析研究所(京都府京都市)
    • Year and Date
      2017-03-06
    • Related Report
      2016 Annual Research Report
  • [Presentation] ベイズモデルの比較による Lindley パラドックスの解消2016

    • Author(s)
      柳本武美,大西俊郎
    • Organizer
      2016年度統計関連学会連合大会
    • Place of Presentation
      金沢大学角間キャンパス(石川県金沢市)
    • Year and Date
      2016-09-04
    • Related Report
      2016 Annual Research Report
  • [Presentation] ベイズ尤度による情報量規準の拡張と改良2015

    • Author(s)
      柳本 武美,大西 俊郎
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      岡山大学(岡山県岡山市)
    • Year and Date
      2015-09-06
    • Related Report
      2015 Research-status Report
  • [Presentation] 変分的手法に基づく尤度およびエントロピーの拡張2015

    • Author(s)
      大西俊郎
    • Organizer
      Statistical Inference on Divergence Measures and Its Related Topics
    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2015-03-10
    • Related Report
      2014 Research-status Report
  • [Presentation] 経験ベイズモデルの超母数の最大ベイズ尤度推定2014

    • Author(s)
      柳本武美, 大西俊郎
    • Organizer
      科研費シンポジウム``空間データと災害の統計モデル"
    • Place of Presentation
      アクロス福岡(福岡県福岡市)
    • Year and Date
      2014-12-21
    • Related Report
      2014 Research-status Report
  • [Presentation] Estimation of running distance of top tennis players from video images and its applications2014

    • Author(s)
      Toshio Sakata, Kosuke Okusa, Hiroyasu Sakamoto, Yukiyasu Yoshinaga, Toshio Ohnishi
    • Organizer
      The 7th International Conference of the European Research Consortium for Informatics and Mathematics Working Group on Computational and Methodological Statistics
    • Place of Presentation
      Pisa, Italy
    • Year and Date
      2014-12-07
    • Related Report
      2014 Research-status Report
  • [Presentation] Duality between likelihood and entropy in Bayesian model averaging2014

    • Author(s)
      Toshio Ohnishi
    • Organizer
      International Statistical Institute Regional Statistics Conference
    • Place of Presentation
      Kuala Lumpur, Malaysia
    • Year and Date
      2014-11-18
    • Related Report
      2014 Research-status Report
  • [Presentation] Bayesモデル平均における尤度とエントロピーの双対性2014

    • Author(s)
      大西俊郎, 柳本武美
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      東京大学(東京都文京区)
    • Year and Date
      2014-09-14
    • Related Report
      2014 Research-status Report
  • [Presentation] ある混合の下でのベイスモデルの尤度2014

    • Author(s)
      柳本武美, 大西俊郎
    • Organizer
      統計関連学会連合大会
    • Place of Presentation
      東京大学(東京都文京区)
    • Year and Date
      2014-09-14
    • Related Report
      2014 Research-status Report

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Published: 2014-04-04   Modified: 2018-03-22  

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