Efficient sampling methods from discrete sampling space of higher dimensions

• Project/Area Number: 18700271
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Statistical science
• Research Institution: Kagoshima University
• Principal Investigator: AOKI Satoshi Kagoshima University, 理学部, 准教授 (90332618)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,630,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: マルコフ連鎖・モンテカルロ法 / グレブナー基底 / マルコフ基底 / 分割表 / トーリックイデアル / 実験計画法 / Segre-Veronese型配置 / 階層モデル / 分割表解析 / マルコフ連鎖モンテカルロ法 / 対称群 / 条件付検定 / 計算機代数統計 / 相似検定 / Segre-Veronese / 一部実施要因計画

Research Abstract

高次元の離散分布からの効率的なサンプリング手法として、マルコフ連鎖を利用したモンテカルロ法を実行するために、以下の3つのテーマに関する研究を行なった。(1)必要となる連結な推移基底(マルコフ基底)の性質解明。(2)純粋数学(代数学)の分野で既存の結果を利用した応用研究。(3)実験計画法の問題に対する定式化と応用研究。

Research Products

• [Journal Article] Some characterizations of affinely full-dimensional factorial designs (2009)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Journal of Statistical Planning and Inference, accepted
  • Peer Reviewed
• [Journal Article] Perturbation method for determining group of invariance of hierarchical models (2009)
  • Author(s): T. Sei, S. Aoki and A. Takemura
  • Journal Title: Advances in Applied Mathematics, accepted
  • Peer Reviewed
• [Journal Article] Markov basis for designed experiments with three-level factors, in Algebraic and Geometric Methods in Statistics (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Mathematical explorations in contemporary statistics, (dedicated to Professor Giovanni Pistone on the occation of his sixty-fifth birthday), edited by P. Gibilisco et al. Pages: 220-233
  • Peer Reviewed
• [Journal Article] Groebner bases of nested configurations (2008)
  • Author(s): S. Aoki, T. Hibi, H. Ohsugi and A. Takemura
  • Journal Title: Journal of Algebra 320 Pages: 2583-2593
  • Peer Reviewed
• [Journal Article] Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections (2008)
  • Author(s): S. Aoki, T. Hibi, H. Ohsugi and A. Takemura
  • Journal Title: Annals of the Institute of Statistical Mathematics, accepted
  • Peer Reviewed
• [Journal Article] Indispensable monomials of toric ideals and Markov bases (2008)
  • Author(s): S. Aoki, A. Takemura and R. Yoshida
  • Journal Title: Journal of Symbolic Computation 43 Pages: 490-507
  • Peer Reviewed
• [Journal Article] The largest group of invariance for Markov bases and toric ideals (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Journal of Symbolic Computation 43 Pages: 342-38
  • Peer Reviewed
• [Journal Article] Minimal invariant Markov basis for samling contingency tables with fixed marginals (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Annals of the Institute of Statistical Mathematics 60 Pages: 229-256
  • Peer Reviewed
• [Journal Article] Minimal invariant Markov basis for sampling contingency tables with fixed marginals (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Annals of the Institute of Statistical Mathematics 60 Pages: 229-256
  • NAID: 40016082023
  • Peer Reviewed
• [Journal Article] The largest group of invariance for Markov bases and to ric ideals (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Journal of Symbolic Computation 43 Pages: 342-358
  • Peer Reviewed
• [Journal Article] Markov basis for design of experiments with three-Level factors (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Algebraic and Geometric Methods in Sta tistics, Mathematical explorations in contemporary statistics (dedicated to Professor Pistone on the occasion of h is sixty-fifth birthday), edited by P. Gibilisco et.al. ISBN : 9780-521-896191 Pages: 220-233
  • Peer Reviewed
• [Journal Article] The largest group of invariance for Markov bases and toric ideals (2008)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Journal of Symbolic computation 43 Pages: 342-358
  • Peer Reviewed
• [Journal Article] Indispensable monomials of toric ideals and Markov bases (2008)
  • Author(s): S. Aoki, A. Takemura and R. Yoshida
  • Journal Title: Journal of Symbolic computation 43 Pages: 490-507
  • Peer Reviewed
• [Journal Article] Markov basis and Grobner basis of Segre-Veronese configuration for Testing independence in group-wise selections (2008)
  • Author(s): S. Aoki, T. Hibi, H. Ohsugi and A. Takemura
  • Journal Title: Annals of the Institute of Statistical Mathematics (In press)
  • NAID: 40017002001
  • Peer Reviewed
• [Journal Article] Statistics and Groebner bases?the origin and development of computational algebraic statistics (2007)
  • Author(s): S. Aoki and A. Takemura
  • Journal Title: Sugaku 59 Pages: 283-302
  • Peer Reviewed
• [Journal Article] Minimal invariant Markov basis for sampling contingency tables with fixed marginals (2007)
  • Author(s): Satoshi Aoki, Akimichi Takemura
  • Journal Title: Annals of the institute of Statistical Mathematics (To appear)
  • NAID: 40016082023
• [Journal Article] Markov chain Monte Carlo tests for designe experiments (2006)
  • Author(s): Satoshi Aoki, AKimichi Takemura
  • Journal Title: METR Technical Report. Department of Mathematical Engineering and Information Physics, The University of Tokyo 2006-56
• [Journal Article] Fibers of sample size two of hierarchical models and Markov bases of decomposable models for contingency tables (2006)
  • Author(s): Hisayuki Hara, Satoshi Aoki, Akimichi Takemura
  • Journal Title: METR Technical Report. Department of Mathematical Engineering and Information Physics, The University of Tokyo 2006-66
• [Journal Article] Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections
  • Author(s): S. Aoki, T. Hibi, H. Ohsugi and A. Takemura
  • Journal Title: Annals of the Institute of Statistical Mathematics (accepted)
  • Peer Reviewed
• [Presentation] Some characterization of affinely full-dimensional factorial design (2008)
  • Author(s): S. Aoki and A. Takemura
  • Organizer: Computational Algebraic Statistics, Th eories and Applications (CASTA2008)
  • Place of Presentation: Kyoto
  • Year and Date: 2008-12-12
• [Presentation] regularでない一部実施計画のあるクラスの性質 (2008)
  • Author(s): 青木敏、竹村彰通
  • Organizer: 日本計算機統計学会第22回シンポジウム、臨床研究情報センター
  • Place of Presentation: 神戸市
  • Year and Date: 2008-11-06
• [Presentation] Regularでない一部実施計画のあるクラスの性質 (2008)
  • Author(s): 青木敏,竹村彰通
  • Organizer: 日本計算機統計学会第22回シンポジウム
  • Place of Presentation: 臨床研究情報センター(神戸市)
  • Year and Date: 2008-11-06
• [Presentation] 3水準の一部実施計画に対するMCMC法による要因効果の検定 (2008)
  • Author(s): 青木敏、竹村彰通
  • Organizer: 2008年度統計関連学会連合大会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2008-09-08
• [Presentation] 一部実施計画における要因の推定可能性と指示関数で表現される交絡の関係 (2008)
  • Author(s): 青木敏、竹村彰通
  • Organizer: 2008年度統計関連学会連合大会
  • Place of Presentation: 慶應義塾大学
  • Year and Date: 2008-09-08
• [Presentation] 3水準の一部実施計画に対するMCMC法による要因効果の検定 (2008)
  • Author(s): 青木敏,竹村彰通
  • Organizer: 2008年度統計関連学会連合連合大会
  • Place of Presentation: 慶應義塾大学(横浜市)
  • Year and Date: 2008-09-08
• [Presentation] 一部実施計画における要因の推定可能性と指示関数で表現される交絡の関係 (2008)
  • Author(s): 青木敏,竹村彰通
  • Organizer: 2008年度統計関連学会連合連合大会
  • Place of Presentation: 慶應義塾大学(横浜市)
  • Year and Date: 2008-09-08
• [Presentation] Markov basis for design of experiments with three-level factors (2008)
  • Author(s): S. Aoki and A. Takemura
  • Organizer: Mathematical explorations in contemporary statistics
  • Place of Presentation: Genova, Italy
  • Year and Date: 2008-05-19
• [Presentation] Some characterization of affinely full-dimensional factorial design (2008)
  • Author(s): S. Aoki and A. Takemura
  • Organizer: Computational Algebraic Statistics, Theories and Applications(CASTA2008)
  • Place of Presentation: Kyoto
• [Presentation] Markov basis for design of experiments with three-level factors (2008)
  • Author(s): S. Aoki and A. Takemura
  • Organizer: Mathematical explorations in contemporary statistics,(dedicated to Professor Giovanni Pistone on the occation of his sixty-fifth birthday)
  • Place of Presentation: Genova
• [Presentation] 一部実施計画に対するMCMC法による要因効果の検定 (2007)
  • Author(s): 青木敏、竹村彰通
  • Organizer: 2007年度統計関連学会連合大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-09-08
• [Presentation] グループごとに制約がある選択問題の条件付検定手法とSegre-Veronese型配置のグレブナー基底 (2007)
  • Author(s): 青木敏、日比孝之、大杉英史、竹村彰通
  • Organizer: 2007年度統計関連学会連合大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-09-08
• [Presentation] 2値入出力系に対する多因子要因効果の検定 (2007)
  • Author(s): 青木敏、宮川雅巳
  • Organizer: 2007年度統計関連学会連合大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-09-08
• [Presentation] 一部実施要因計画に対するMCMC法による要因効果の検定 (2007)
  • Author(s): 青木敏、竹村彰通
  • Organizer: 2007年度統計関連学会連合大会
  • Place of Presentation: 神戸大学
  • Year and Date: 2007-09-08
• [Presentation] グループごとに制約がある選択問題の条件付検定手法とSegre-Veronese型配置のグレブナー基底 (2007)
  • Author(s): 青木敏、日比孝之、大杉英史、竹村彰通
  • Organizer: 日本数学会2007年度年会
  • Place of Presentation: 埼玉大学
  • Year and Date: 2007-03-29