Theory of Bayesian Multiscale Bootstrap and its Applications

• Project/Area Number: 20500254
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Statistical science
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: SHIMODAIRA Hidetoshi Tokyo Institute of Technology, 大学院・情報理工学研究科, 准教授 (00290867)
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2008: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
• Keywords: リサンプリング / マルチスケール / スケーリング則 / 仮説検定 / 信頼度 / 機械学習 / バイオインフォマティクス / モデル選択 / ブートストラップ / アルゴリズム / 統計数学 / 系統進化 / 統計的仮説検定 / ランダムネス

Research Abstract

A resampling algorithm based on a scaling-law of randomness has been studied for computing a highly accurate confidence level of data analysis. In a previous study, we have proposed multiscale bootstrap method which computes an approximately unbiased confidence level (p-value) of statistical hypothesis testing in a frequentist sense. In this study, we proposed a method for computing the posterior probability in a Bayesian sense. We have shown a connection between the frequentist and the Bayesian confidence levels. We also studied a confidence level, as well as an active learning, for machine learning using the scaling-law of the randomness.

Research Products

• [Journal Article] A scale-free structure prior for graphical models with applications in functional genomics (2010)
  • Author(s): P.Sheridan, T.Kamimura, H.Shimodaira
  • Journal Title: PLoS ONE 5
  • Peer Reviewed
• [Journal Article] Frequentist and Bayesian measures of confidence viamultiscale bootstrap for testing three regions (2010)
  • Author(s): Hidetoshi Shimodaira
  • Journal Title: Annals of the Institute of Statistical Mathematics 62 Pages: 189-208
  • NAID: 40016969858
  • Peer Reviewed
• [Journal Article] A scale-free structure prior for graphical models with applications in functional genomics (2010)
  • Author(s): P.Sheridan
  • Journal Title: PLoS ONE Volume: 5
  • Peer Reviewed
• [Journal Article] Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions (2010)
  • Author(s): Hidetoshi Shimodaira
  • Journal Title: Annals of the Institute of Statistical Mathematics 62 Pages: 189-208
  • NAID: 40016969858
  • Peer Reviewed
• [Presentation] Multiscale Bagging with Applications to Classification and Active Learning (2010)
  • Author(s): H.Shimodaira
  • Organizer: The 2nd Asian Conference on Machine Learning(ACML2010)
  • Place of Presentation: 東工大 (東京)
  • Year and Date: 2010-11-10
• [Presentation] Multiscale-bagging with Applications to Classification (2010)
  • Author(s): M.Aoki
  • Organizer: The 2nd Asian Conference on Machine Learning (ACM L2010)
  • Place of Presentation: 東工大 (東京)
  • Year and Date: 2010-11-10
• [Presentation] Multiscale-bagging with Applications to Classification (2010)
  • Author(s): M.Aoki
  • Organizer: The 2nd Asian Conference on Machine Learning (ACML2010)
  • Place of Presentation: 東工大(東京)
  • Year and Date: 2010-11-10
• [Presentation] Multiscale Bagging with Applications to Classification and Active Learning (2010)
  • Author(s): H.Shimodaira
  • Organizer: The 2nd Asian Conference on Machine Learning (ACML2010)
  • Place of Presentation: 東工大(東京)
  • Year and Date: 2010-11-10
• [Presentation] Assessing statistical reliability of LiNGAM via multiscale bootstrap (2010)
  • Author(s): Y.Komatsu
  • Organizer: International Conference on Artificial Neural Networks(ICANN2010)
  • Place of Presentation: Thessaloniki(ギリシャ)
  • Year and Date: 2010-09-15
• [Presentation] Assessing statistical reliability of LiNGAM via multiscale boostrap (2010)
  • Author(s): Y.Komatsu
  • Organizer: International Conference on Artificial Neural Networks (ICANN2010)
  • Place of Presentation: Thessaloniki(ギリシャ)
  • Year and Date: 2010-09-15
• [Presentation] 不完全データにおける情報量規準の状態空間モデルへの応用 (2010)
  • Author(s): 青井遥
  • Organizer: 2010年度 統計関連学会連合大会
  • Place of Presentation: 早稲田大学(東京)
  • Year and Date: 2010-09-07
• [Presentation] マルチスケール・ブートストラップ法を用いたQuery by baggingの改良 (2010)
  • Author(s): 三根宏太
  • Organizer: 2010年度 統計関連学会連合大会
  • Place of Presentation: 早稲田大学(東京)
  • Year and Date: 2010-09-06
• [Presentation] ブートストラップ確率の計算誤差を修正するためのマルチスケール・ブートストラップ法:LiNGAM因果構造推定の場合 (2010)
  • Author(s): 小松勇介
  • Organizer: 2010年度 統計関連学会連合大会
  • Place of Presentation: 早稲田大学(東京)
  • Year and Date: 2010-09-06
• [Presentation] 系統樹推定におけるブートストラップ法 (2010)
  • Author(s): 下平英寿
  • Organizer: 日本進化学会第12回 東京大会
  • Place of Presentation: 東工大(東京)
  • Year and Date: 2010-08-03
• [Presentation] 多数の片側検定に関するFalse Discovery Rateのマルチスケール計算 (2009)
  • Author(s): 下平英寿
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-08
• [Presentation] マルチスケール・バギングによる判別分析の信頼性評価 (2009)
  • Author(s): 青木正良
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-08
• [Presentation] マルチスケール・ブトストラップを用いた信頼度計算:LiNGAMによる因果モデル探索の場合 (2009)
  • Author(s): 小松勇介
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 同志社大学
  • Year and Date: 2009-09-07
• [Presentation] Approximately unbiased tests for cone shaped regions via multiscale bootstrap (2009)
  • Author(s): Hidetoshi Shimodaira
  • Organizer: 2009 Annual Meeting, Statistical Society of Canada
  • Place of Presentation: The University of British Columbia(カナダ)
  • Year and Date: 2009-06-03
• [Presentation] Approximately unbiased tests for cone shaped regions via multiscale bootstrap (2009)
  • Author(s): Hidetoshi Shimodaira
  • Organizer: 2009 Annual Meeting, Statistical Society of Canada
  • Place of Presentation: The University of British Columbia
  • Year and Date: 2009-06-03
• [Presentation] マルチスケール・ブートストラップ法によるランダムネスの測定 (2009)
  • Author(s): 下平英寿
  • Organizer: 統計学会春季集会
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2009-03-06
• [Presentation] Measuring the Randomness of Data via Multiscale Bootstrap with Applications to Evolutionary Tree Inference (2009)
  • Author(s): Hidetoshi Shimodaira
  • Organizer: International Symposium of Case Studies involving Statistics and Operations Research for Decision Making
  • Place of Presentation: 統計数理研究所
  • Year and Date: 2009-03-02
• [Presentation] Frequentist and Bayesian measures of confidence via multiscale bootstrap for testing three regions (2008)
  • Author(s): Hidetoshi Shimodaira
  • Organizer: A Bayesian Approach to Statistical Inference and Its Related Topics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-10-22
• [Presentation] Frequentist and Bayesian measures of confidence viamultiscale bootstrap for testing three regions (2008)
  • Author(s): Hidetoshi Shimodaira
  • Organizer: A Bayesian Approach to Statistical Inference and Its Related Topics
  • Place of Presentation: 京都大学数理解析研究所
  • Year and Date: 2008-10-22
• [Presentation] マルチスケール・ブートストラップ法による頻度論的およびベイズ的な信頼度計算 (2008)
  • Author(s): 下平英寿
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2008-09-09
• [Presentation] Rを用いたブートストラップ法の大規模並列計算 (2008)
  • Author(s): 下平英寿
  • Organizer: 統計関連学会連合大会
  • Place of Presentation: 慶応義塾大学
  • Year and Date: 2008-09-09
• [Book] 21世紀の統計科学III数理・計算の統計科学 (2008)
  • Author(s): 竹村彰通, 北川源四郎, 藤越康祝, 久保川達也, 塚原英敦, 田中勝人, 内田雅之, 下平英寿, 渡辺美智子, 古澄英男, 生駒哲一
  • Publisher: 東京大学出版会
• [Book] 21世紀の統計科学I I I 数理・計算の統計科学 (2008)
  • Author(s): 竹村彰通, 北川源四郎, 藤越康祝, 久保川達也, 塚原英敦, 田中勝人, 内田雅之, 下平英寿, 渡辺美智子, 古澄英男, 生駒哲一
  • Publisher: 東京大学出版会
• [Remarks] ホームページ
  • URL: http://www.is.titech.ac.jp/~shimo/index-j.html
• [Remarks] 大田区の区民大学(東京工業大学連携講座)「DNA情報からよみとる生物進化とランダムネス」
  • URL: http://www.is.titech.ac.jp/~shimo/kumin2010/index-i.html
• [Remarks]
  • URL: http://www.is.titech.ac.jp/~shimo/index-j.html
• [Remarks]
  • URL: http://www.is.titech.ac.jp/~shimo/index-j.html