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Developments of mathematical statistics through computational algebraic methods

Research Project

Project/Area Number 22240029
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionThe University of Tokyo

Principal Investigator

TAKEMURA Akimichi  東京大学, 情報理工学(系)研究科, 教授 (10171670)

Co-Investigator(Renkei-kenkyūsha) AOKI Satoshi  鹿児島大学, 理工学研究科, 准教授 (90332618)
IWASAKI Manabu  成蹊大学, 理工学部, 教授 (40255948)
EGUCHI Shinto  大学共同利用機関法人 情報・システム研究機構, 統計数理研究所 数理・推論研究系, 教授 (10168776)
OHSUGI Hidefumi  立教大学, 理学部, 准教授 (80350289)
KAMIYA Hidehiko  名古屋大学, 経済学研究科, 教授 (50300687)
KURIKI Satoshi  大学共同利用機関法人 情報・システム研究機構, 統計数理研究所 数理・推論研究系, 教授 (90195545)
KOMAKI Fumiyasu  東京大学, 情報理工学(系)研究科, 教授 (70242039)
SAKATA Toshio  九州大学, 芸術工学研究院, 教授 (20117352)
TANIGUCHI Masanobu  早稲田大学, 理工学術院, 教授 (00116625)
HARA Hisayuki  新潟大学, 経済学部, 准教授 (40312988)
HIBI Takayuki  大阪大学, 情報科学研究科, 教授 (80181113)
YOSHIZOE Yasuto  青山学院大学, 経済学部, 教授 (80062868)
Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥49,270,000 (Direct Cost: ¥37,900,000、Indirect Cost: ¥11,370,000)
Fiscal Year 2013: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000)
Fiscal Year 2012: ¥9,620,000 (Direct Cost: ¥7,400,000、Indirect Cost: ¥2,220,000)
Fiscal Year 2011: ¥19,240,000 (Direct Cost: ¥14,800,000、Indirect Cost: ¥4,440,000)
Fiscal Year 2010: ¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000)
Keywordsマルコフ連鎖モンテカルロ法 / トーリックイデアル / グレブナー基底 / 条件つき検定 / 超平面配置
Research Abstract

In this project we obtained many important results. The most notable one is the success of the second Institute of Mathematical Statistics Pacific Rim Meeting, held in Tsukuba City during July 1-4 of 2012. The principal investigator of this project was responsible for this important conference in mathematical statistics.
Also the principal investigator with Satoshi Aoki and Hisayuki Hara published "Markov bases in Algebraic Statistics" from Springer in 2012.

Report

(4 results)
  • 2013 Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (43 results)

All 2013 2012 2011 2010 Other

All Journal Article (21 results) (of which Peer Reviewed: 21 results) Presentation (18 results) (of which Invited: 8 results) Book (1 results) Remarks (3 results)

  • [Journal Article] Holonomic gradient method for the distribution function of the largest root of a Wishart matrix2013

    • Author(s)
      Hiroki Hashiguchi, Yasuhide Numata, Nobuki Takayama and A. Takemura
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 117 Pages: 296-312

    • DOI

      10.1016/j.jmva.2013.03.011

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Properties and applications of Fisher distribution on the rotation group2013

    • Author(s)
      Tomonari Sei, Hiroki Shibata, A. Takemura, Katsuyoshi Ohara and Nobuki Takayama
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 116 Pages: 440-455

    • DOI

      10.1016/j.jmva.2013.01.010

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A lower bound for the Graver complexity of the incidence matrix of a complete bipartite graph2012

    • Author(s)
      Taisei Kudo and A. Takemura
    • Journal Title

      Journal of Combinatorics

      Volume: 3, No.4 Pages: 695-708

    • URL

      http://intlpress.com/site/pub/pages/journals/items/joc/content/vols/0003/0004/a007/index.html

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On intersection lattices of hyperplane arrangements generated by generic points2012

    • Author(s)
      Hiroshi Koizumi, Yasuhide Numata and A. Takemura
    • Journal Title

      Annals of Combinatoris

      Volume: 16 Issue: 4 Pages: 789-813

    • DOI

      10.1007/s00026-012-0161-6

    • Related Report
      2013 Final Research Report 2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Arrangements stable under the Coxeter groups2012

    • Author(s)
      Hidehiko Kamiya, A.Takemura and Hiroaki Terao
    • Journal Title

      Configuration Spaces: Geometry, Combinatorics and Topology

      Volume: 1 Pages: 327-354

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of non-central integral arrangements modulo positive integers2011

    • Author(s)
      Hidehiko Kamiya, A. Takemura and Hiroaki Terao
    • Journal Title

      Annals of Combinatorics

      Volume: 15 Issue: 3 Pages: 449-464

    • DOI

      10.1007/s00026-011-0105-6

    • NAID

      120006459602

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Markov basis for two-state toric homogeneous Markov chain model without initial parameters2011

    • Author(s)
      Hisayuki Hara and A. Takemura
    • Journal Title

      Journal of the Japan Statistical Society

      Volume: 41 Pages: 33-49

    • NAID

      10029335244

    • URL

      http://www.terrapub.co.jp/journals/jjss/frame/41.html

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Holonomic gradient descent and its application to the Fisher-Bingham integral2011

    • Author(s)
      Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara, Tomonari Sei, Nobuki Takayama and A. Takemura
    • Journal Title

      Advances in Applied Mathematics

      Volume: 47 Issue: 3 Pages: 639-658

    • DOI

      10.1016/j.aam.2011.03.001

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Ranking patterns of unfolding models of codimension one2011

    • Author(s)
      Hidehiko Kamiya, A. Takemura and Hiroaki Terao
    • Journal Title

      Advances in Applied Mathematics

      Volume: 47 Issue: 2 Pages: 379-400

    • DOI

      10.1016/j.aam.2010.11.002

    • NAID

      120003207598

    • Related Report
      2013 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Markov basis for two-state toric homogeneous Markov chain model without initial parameters2011

    • Author(s)
      Hisayuki Hara, A.Takemura
    • Journal Title

      Journal of the Japan Statistical Society

      Volume: 41 Pages: 33-49

    • NAID

      10029335244

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Properties of semi-elementary imsets as sums of elementary imsets2011

    • Author(s)
      Takuya Kashimura, Tomonari Sei, A. Takemura, Kentaro Tanaka
    • Journal Title

      Journal of Algebraic Statistics

      Volume: 2 Pages: 14-35

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 大学入試センター試験科目選択データの統計解析2010

    • Author(s)
      青木敏, 大津起夫, 竹村彰通, 沼田泰英
    • Journal Title

      応用統計学

      Volume: 39 Pages: 71-100

    • NAID

      10027618146

    • URL

      https://www.jstage.jst.go.jp/article/jappstat/39/2_3/39_2_3_71/_article/-char/ja/

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Connecting tables with zero-one entries by a subset of a Markov basis. in Algebraic Methods in Statistics and Probability II, (M.A.G.Viana and H.P.Wynn, eds.)2010

    • Author(s)
      Hisayuki Hara and A. Takemura
    • Journal Title

      Contemporary Mathematics

      Volume: vol.516 Pages: 199-213

    • URL

      http://www.ams.org/books/conm/516/

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] A localization approach to improve iterative proportional scaling in Gaussian graphical models2010

    • Author(s)
      Hisayuki Hara and A. Takemura
    • Journal Title

      Communications in Statistics Theory and Methods

      Volume: 39, No.8 Issue: 8-9 Pages: 1643-1654

    • DOI

      10.1080/03610920802238662

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Minimal and minimal invariant Markov bases of decomposable models for contingency tables2010

    • Author(s)
      Hisayuki Hara, Satoshi Aoki and A. Takemura
    • Journal Title

      Bernoulli

      Volume: 16, No.1 Issue: 1 Pages: 208-233

    • DOI

      10.3150/09-bej207

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] On connectivity of fibers with positive marginals in multiple logistic regression2010

    • Author(s)
      Hisayuki Hara, A. Takemura and Ruriko Yoshida
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Issue: 4 Pages: 909-925

    • DOI

      10.1016/j.jmva.2009.12.014

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 大学入試センター試験科目選択データの統計解析2010

    • Author(s)
      青木 敏,大津起夫, 竹村彰通, 沼田泰英
    • Journal Title

      応用統計学会誌

      Volume: 39 Pages: 71-100

    • NAID

      10027618146

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Connecting tables with zero-one entries by a subset of a Markov basis.2010

    • Author(s)
      Hisayuki Hara, A.Takemura
    • Journal Title

      Algebraic Methods in Statistics and Probability II

      Volume: 516 Pages: 199-213

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A localization approach to improve iterative proportional scaling in Gaussian graphical models.2010

    • Author(s)
      Hisayuki Hara, A.Takemura
    • Journal Title

      Communications in Statistics Theory and Methods

      Volume: 39 Pages: 1643-1654

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Minimal and minimal invariant Markov bases of decomposable models for contingency tables.2010

    • Author(s)
      Hisayuki Hara, Satoshi Aoki, A.Takemura
    • Journal Title

      Bernoulli

      Volume: 16 Pages: 208-233

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On connectivity of fibers with positive marginals in multiple logistic .regression.2010

    • Author(s)
      Hisayuki Hara, A.Takemura, Ruriko Yoshida.
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 101 Pages: 909-925

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Introduction to the Holonomic Gradient Method in Statistics2013

    • Author(s)
      竹村彰通
    • Organizer
      Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO, Busan, Korea
    • Year and Date
      2013-07-01
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Aims and structure of Japan Statistical Society Certificate2012

    • Author(s)
      竹村彰通
    • Organizer
      Korean Statistical Society fall meeting
    • Place of Presentation
      Konkuk University, Seoul, Korea
    • Year and Date
      2012-11-03
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ウィシャート分布に現れる行列変数の超幾何関数に対するホロノミック勾配法2012

    • Author(s)
      竹村彰通
    • Organizer
      超幾何方程式研究会
    • Place of Presentation
      神戸大学
    • Year and Date
      2012-01-06
    • Related Report
      2011 Annual Research Report
  • [Presentation] ウィシャート分布に現れる行列変数の超幾何関数に対するホロノミック勾配法2012

    • Author(s)
      竹村彰通
    • Organizer
      研究集会「超幾何方程式研究会」
    • Place of Presentation
      神戸大学(兵庫県)
    • Related Report
      2013 Final Research Report
  • [Presentation] A review of conditional independence inferences based on imsets2011

    • Author(s)
      竹村彰通
    • Organizer
      Statistics Department
    • Place of Presentation
      University of British Columbia, カナダ
    • Year and Date
      2011-08-09
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] A review of conditional independence inferences based on imsets2011

    • Author(s)
      竹村彰通
    • Organizer
      University of British Columbia stat seminar
    • Place of Presentation
      University of British Columbia・バンクーバー・カナダ(招待講演)
    • Year and Date
      2011-08-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Some recent results on ranking patterns and arrangements2011

    • Author(s)
      竹村彰通
    • Organizer
      workshop "Hyperplane arrangements and applications"
    • Place of Presentation
      University of British Columbia, カナダ
    • Year and Date
      2011-08-08
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Some recent results on ranking patterns and arrangements2011

    • Author(s)
      竹村彰通
    • Organizer
      Hyperplane arrangements and applications
    • Place of Presentation
      University of British Columbia・バンクーバー・カナダ(招待講演)
    • Year and Date
      2011-08-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Holonomic Gradient Descent Method For Evaluation of Maximum Likelihood Estimate of an Exponential Family and Its Application to Directional Statistics2010

    • Author(s)
      竹村彰通
    • Organizer
      2010 Annual Meeting of Chinese Statistical Society and International Statistical Conference
    • Place of Presentation
      Jhongli, Taiwan
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Ranking Patterns of Unfolding Models of Codimension One2010

    • Author(s)
      竹村彰通
    • Organizer
      Workshop on Statistics Frongiers 2010 ISS
    • Place of Presentation
      Activity Center, Academia sinica, Taiwan
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] マルコフ連鎖のhomogeneity の正確検定について2010

    • Author(s)
      原尚幸, 竹村彰通
    • Organizer
      統計関連連合学会
    • Place of Presentation
      早稲田大学(東京都)
    • Related Report
      2013 Final Research Report
  • [Presentation] Holonomic Gradient Descent Method For Evaluation of Maximum Likelihood Estimate of an Exponential Family and Its Application to Directional Statistics2010

    • Author(s)
      Akimichi Takemura, Tomonari Sei, Nobuki, Takayama, Hiromasa Nakayama, Kenta Nishiyama, Masayuki Noro, Katsuyoshi Ohara
    • Organizer
      The 2010 Annual Meeting of Chinese Statistical Society and International Statistical Conference
    • Place of Presentation
      Jhongli, Taiwan
    • Related Report
      2010 Annual Research Report
  • [Presentation] Ranking Patterns of Unfolding Models of Codimension One2010

    • Author(s)
      Akimichi Takemura
    • Organizer
      Workshop on Statistics Frontiers 2010 ISS
    • Place of Presentation
      Academia Sinica, Taiwan
    • Related Report
      2010 Annual Research Report
  • [Presentation] マルコフ連鎖のhomogeneityの正確検定について2010

    • Author(s)
      原尚幸, 竹村彰通
    • Organizer
      統計関連連合学会
    • Place of Presentation
      早稲田大学早稲田キャンパス
    • Related Report
      2010 Annual Research Report
  • [Presentation] "Introduction to the Holonomic Gradient Method in Statistics"

    • Author(s)
      竹村 彰通
    • Organizer
      Asian Mathematical Conference 2013
    • Place of Presentation
      BEXCO・釜山・韓国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] "Non-linear autoregressive models with time-varying coefficients and volatility for minimum temperature with applications in agrorisk analysis"

    • Author(s)
      Reza Hosseini
    • Organizer
      ISF 2013
    • Place of Presentation
      KAIST College of Business・ソウル・韓国
    • Related Report
      2012 Annual Research Report
  • [Presentation] "Birkhoff モデルのマルコフ次元"

    • Author(s)
      山口 天
    • Organizer
      応用統計学会2013年度年会
    • Place of Presentation
      パルセいいざか・福島県飯坂市
    • Related Report
      2012 Annual Research Report
  • [Presentation] "Aims and structure of Japan Statistical Society Certificate"

    • Author(s)
      竹村 彰通
    • Organizer
      Korean Statistical Society fall meeting
    • Place of Presentation
      Konkuk University・ソウル・韓国
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Book] Markov Bases in Algebraic Statistics2012

    • Author(s)
      青木敏, 原尚幸, 竹村彰通
    • Total Pages
      298
    • Publisher
      Springer
    • Related Report
      2013 Final Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/kakenhi/h22ka/

    • Related Report
      2013 Final Research Report
  • [Remarks] 科学研究費「計算代数手法に基づく数理統計学の展開」 基盤研究 (A) 22240029

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/kakenhi/h22ka/

    • Related Report
      2012 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/atstat/kakenhi/h22ka/

    • Related Report
      2011 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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