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An application of computational algebraic methods to the theory of statistical experimental designs

Research Project

Project/Area Number 23500355
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Statistical science
Research InstitutionKobe University (2015-2016)
Kagoshima University (2011-2014)

Principal Investigator

Aoki Satoshi  神戸大学, 理学研究科, 教授 (90332618)

Research Collaborator Takemura Akimichi  
Hibi Takayuki  
Ohsugi Hidefumi  
Project Period (FY) 2011-04-28 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywords実験計画法 / グレブナー基底 / 計算代数 / イデアル / 分割表 / マルコフ連鎖モンテカルロ法 / 計算代数統計 / 一部実施計画 / 検定 / 多因子実験 / マルコフ基底 / 統計的実験計画法 / トーリックイデアル
Outline of Final Research Achievements

In the field of the computaional algebraic statistics, applications of the Groebner basis theory to various statistical problems are considered, mainly in the context of contingency tables since 1990's. In this research, we aimed to present new statistical models and methods in the context of statistical experimental designs, which is one of the important topics in the applied statistics. Our results include new statistical models for non-normalized data, and are based on the theory of the structure of the ideals in the polynomial rings.

Report

(7 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (32 results)

All 2017 2016 2015 2014 2013 2012 2011 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (24 results) (of which Int'l Joint Research: 7 results,  Invited: 5 results) Book (3 results)

  • [Journal Article] Markov bases for two-way change-point models of ladder determinantal tables2017

    • Author(s)
      Satoshi Aoki and Takayuki Hibi
    • Journal Title

      Journal of Algebraic Statistics

      Volume: 印刷中

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations2016

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: 10 Issue: 1 Pages: 59-72

    • DOI

      10.1080/15598608.2015.1067172

    • Related Report
      2016 Annual Research Report 2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Minimal Markov basis for tests of main effect models for $2^{p-1}$ fractional factorial designs of resolution $p$2015

    • Author(s)
      S. Aoki
    • Journal Title

      Communication in Statistics, Simulation and Computation

      Volume: 44 Issue: 9 Pages: 2371-2386

    • DOI

      10.1080/03610918.2014.906609

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals2013

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Journal Title

      J. Statist. Plann. Inference

      Volume: 143 Issue: 10 Pages: 1791-1806

    • DOI

      10.1016/j.jspi.2013.06.009

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Design and analysis of fractional factorial pppexperiments from the viewpoint of computational algebraic statistics2012

    • Author(s)
      Aoki, S. and Takemura,A.
    • Journal Title

      Journal of Statistical Theory and Practice

      Volume: VOL.6 Issue: 1 Pages: 147-161

    • DOI

      10.1080/15598608.2012.647556

    • Related Report
      2012 Research-status Report 2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Markov bases for two-way change-point models of ladder determinantal tables2016

    • Author(s)
      Satoshi Aoki
    • Organizer
      RIMS seminar, Binomial Ideals and Algebraic Statistics
    • Place of Presentation
      関西セミナーハウス (京都府・京都市)
    • Year and Date
      2016-10-31
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Algebraic construction of two-level fractional factorial designs2016

    • Author(s)
      青木敏
    • Organizer
      2016年度統計関連学会連合大会
    • Place of Presentation
      金沢大学 (石川県・金沢市)
    • Year and Date
      2016-09-05
    • Related Report
      2016 Annual Research Report
  • [Presentation] Algebraic construction of two-level fractional factorial designs2016

    • Author(s)
      Satoshi Aoki
    • Organizer
      RIMS Workshop, Algebraic Statistics and Symbolic Computation
    • Place of Presentation
      京都大学数理解析研究所 (京都府・京都市)
    • Year and Date
      2016-07-25
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Sampling methods of fractional factorial designs.2016

    • Author(s)
      Satoshi Aoki
    • Organizer
      The 4th Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      The Chinese University of Hong Kong, Hong Kong
    • Year and Date
      2016-06-27
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Algebraic construction of two-level fractional factorial designs2016

    • Author(s)
      Satoshi Aoki
    • Organizer
      RIMS Workshop, Application of Algebraic Methods to Statistics (AAMS 2016)
    • Place of Presentation
      京都大学数理解析研究所 (京都府・京都市)
    • Year and Date
      2016-06-20
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations2016

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Organizer
      The 4th Japan-Taiwan Conference on Combinatorics and its Applications
    • Place of Presentation
      北九州国際会議場(福岡県・北九州市)
    • Year and Date
      2016-03-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] マルコフ連鎖モンテカルロ法による Box-Behnken計画の解析と中心対称配置2015

    • Author(s)
      青木敏,日比孝之,大杉英史
    • Organizer
      数学会秋季総合分科会
    • Place of Presentation
      京都産業大学(京都府・京都市)
    • Year and Date
      2015-09-16
    • Related Report
      2015 Research-status Report
  • [Presentation] マルコフ連鎖モンテカルロ法によるBox-Behnken計画の解析と中心対称配置2015

    • Author(s)
      青木敏,日比孝之,大杉英史
    • 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
      2015-09-09
    • Related Report
      2015 Research-status Report
  • [Presentation] Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations2015

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Organizer
      SIAM Conference on Applied Algebraic Geometry
    • Place of Presentation
      NIMS, Daejeon, Korea
    • Year and Date
      2015-08-05
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Markov chain Monte Carlo methods for the Box-Behnken designs and centrally symmetric configurations2015

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Organizer
      The 8th MSJ-SI 2015, Mathematical Society of Japan, Seasonal Institute, ``Current Trends on Groebner Bases --- The 50th Anniversary of Groebner Bases---"
    • Place of Presentation
      ホテル日航大阪(大阪府・大阪市)
    • Year and Date
      2015-07-07
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Sampling fractional factorial designs by Markov basis2014

    • Author(s)
      Satoshi Aoki
    • Organizer
      AISC2014 (International Conference on Advances in Interdisciplinary Statistics and Combinatorics)
    • Place of Presentation
      The University of North Carolina Greensboro, NC, USA
    • Year and Date
      2014-10-10 – 2014-10-12
    • Related Report
      2014 Research-status Report
  • [Presentation] マルコフ基底をもちいた一部実施計画のサンプリング2014

    • Author(s)
      青木敏
    • Organizer
      2014年度統計関連学会連合大会
    • Place of Presentation
      東京大学、東京
    • Year and Date
      2014-09-13 – 2014-09-16
    • Related Report
      2014 Research-status Report
  • [Presentation] Markov Bases in Statistics2014

    • Author(s)
      青木敏
    • Organizer
      2014年度統計関連学会連合大会
    • Place of Presentation
      東京大学、東京
    • Year and Date
      2014-09-13 – 2014-09-16
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Markov chain Monte Carlo methods for regular two-level fractional factorial designs and cut ideals2014

    • Author(s)
      Satoshi Aoki
    • Organizer
      CEDA2014 (Conference on Experimental Design and Analysis 2014)
    • Place of Presentation
      Howard Civil Service International House, Taipei, Taiwan
    • Year and Date
      2014-07-04 – 2014-07-05
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Sampling fractional factorial designs by Markov basis2014

    • Author(s)
      Satoshi Aoki
    • Organizer
      The 3rd Institute of Mathematical Statistics Asia Pacific Rim Meeting
    • Place of Presentation
      Howard Civil Service International House, Taipei, Taiwan
    • Year and Date
      2014-06-29 – 2014-07-03
    • Related Report
      2014 Research-status Report
  • [Presentation] 2水準実験に対するマルコフ連鎖モンテカルロ法と切断イデアル2013

    • Author(s)
      青木敏、大杉英史、日比孝之
    • Organizer
      日本数学会2013年年会
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Markov chain Monte Carlo tests for regular fractional factorial designs and cut ideals2012

    • Author(s)
      S. Aoki
    • Organizer
      International Conference on Advances in Interdisciplinary Statistics and Combinatorics
    • Place of Presentation
      The University of North Carolina, Greensboro, NC
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Algebraic methods for design of experiments2012

    • Author(s)
      S. Aoki
    • Organizer
      2012年度統計関連学会連合大会
    • Place of Presentation
      北海道大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Minimal Markov basis for tests of main effects model for 2^{p-1} fractional factorial designs2011

    • Author(s)
      Satoshi Aoki
    • Organizer
      International Conference on Advances in Probability and Statistics(招待講演)
    • Place of Presentation
      Hong Kong SAR
    • Related Report
      2011 Research-status Report
  • [Presentation] 大学入試センター試験科目選択データの統計解析2011

    • Author(s)
      青木敏、大津起夫、竹村彰通、沼田泰英
    • Organizer
      応用統計学会・大学入試センター「学力試験データの統計解析」特集号ワークショップ(招待講演)
    • Place of Presentation
      成蹊大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 実験計画法とグレブナー基底2011

    • Author(s)
      青木敏
    • Organizer
      2011年度統計関連学会連合大会
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Sampling fractional factorial designs by Markov basis

    • Author(s)
      S. Aoki
    • Organizer
      Computational Algebraic Statistics, Theories and Applications (CASTA2014)
    • Place of Presentation
      Kyoto (京都テルサ)
    • Related Report
      2013 Research-status Report
  • [Presentation] Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals

    • Author(s)
      S. Aoki, T. Hibi and H. Ohsugi
    • Organizer
      Designs, Codes, Graphs and Related Areas, RIMS
    • Place of Presentation
      Kyoto (京都大学)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 2水準実験に対するマルコフ連鎖モンテカルロ法と切断イデアル

    • Author(s)
      青木敏, 大杉英史, 日比孝之
    • Organizer
      2013年度統計関連学会連合大会
    • Place of Presentation
      大阪大学
    • Related Report
      2013 Research-status Report
  • [Book] 東京大学工学教程 確率・統計II2016

    • Author(s)
      青木敏、竹村彰通
    • Total Pages
      166
    • Publisher
      丸善出版株式会社
    • Related Report
      2015 Research-status Report
  • [Book] Markov Bases in Algebraic Statistics2012

    • Author(s)
      S. Aoki, H. Hara, A. Takemura
    • Total Pages
      293
    • Publisher
      Springer Series in Statistics
    • Related Report
      2012 Research-status Report
  • [Book] マルコフ基底と実験計画法、グレブナー道場2011

    • Author(s)
      青木敏、竹村彰通 (JST CREST 日比チーム[編])
    • Total Pages
      560
    • Publisher
      共立出版
    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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