Statistical inference on discrete patterns on random structures

• Project/Area Number: 22540159
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Kansai University
• Principal Investigator: AKI Sigeo 関西大学, システム理工学部, 教授 (90132696)
• Project Period (FY): 2010-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000); 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); Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: 統計数学 / 条件付き確率母関数 / 離散パターン / DAG / グラフィカルモデル / システムの信頼度 / マルコフ性 / 生存時間 / 連 / クーポン集め問題 / 可換性 / De Finetti の定理 / 順位付け / 尤度比検定 / 対称群 / 隣接リスト / システムの信頼性 / 連続システム / de Finetti測度 / Fibonacci多項式 / マーク付き点過程 / 可換系列 / 経験分布関数 / オーダーkの離散分布 / Markov可換性 / 確率母関数

Research Abstract

Main results of the research are as follows. A method for deriving exact distributions of numbers of discrete patterns observed on undirected graphical models is proposed. Parametric statistical models are proposed for observed discrete patterns on exchangeable or partially exchangeable sequences of trials. The mixing measures of the exchangeable sequences also obtained. Further, a parametric statistical model on the permutation group is proposed by using the coupon collecter's problems. The statistical model is useful for statistical inference of ranking data such as maximum likelihood estimation and likelihood ratio tests.

Research Products

• [Journal Article] Coupon collector's problems with statistical applications to rankings (2013)
  • Author(s): Aki, S. and Hirano, K.
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: Vol.65 Issue: 3 Pages: 571-587
  • DOI: 10.1007/s10463-012-0382-9
  • NAID: 40019656401
  • Peer Reviewed
• [Journal Article] Distributions of numbers of runs and scans on directed acyclic graphs with generation (2013)
  • Author(s): Inoue, K. and Aki, S.
  • Journal Title: Computational Statistics Volume: 28 Issue: 3 Pages: 1133-1150
  • DOI: 10.1007/s00180-012-0349-6
  • Peer Reviewed
• [Journal Article] Generating Functions of Waiting Times and Numbers of Visits for Random Walks on Graphs (2013)
  • Author(s): Kiyoshi Inoue, Aki, S. and Balakrishnan Narayanaswamy
  • Journal Title: Methodology and Computing in Applied Probability Volume: 15 Issue: 2 Pages: 349-362
  • DOI: 10.1007/s11009-011-9246-7
  • Peer Reviewed
• [Journal Article] Statistical modeling for discrete patterns in a sequence of exchangeable trials (2012)
  • Author(s): Aki, S.
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: Vol.64 Issue: 3 Pages: 633-655
  • DOI: 10.1007/s10463-011-0325-x
  • NAID: 40019169149
  • Peer Reviewed
• [Journal Article] Exact distributions of the number of pattern occurrences in undirected graphical models (2012)
  • Author(s): Aki, S. and Inoue, K.
  • Volume: Vol.42
  • Pages: 59-79
  • NAID: 10030867431
  • URL: http://www.terrapub.co.jp/journals/jjss/frame/42.html
  • Peer Reviewed
• [Journal Article] Exact distributions of the number of pattern occurrences in undirected graphical models (2012)
  • Author(s): Aki, S. and Inoue, K.
  • Journal Title: Journal of Japan Statistical Society Volume: 42 Pages: 59-79
  • NAID: 10030867431
  • Peer Reviewed
• [Journal Article] Bivariate Fibonacci polynomials of order k with statistical applications (2011)
  • Author(s): Inoue, K. and Aki, S.
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: Vol.63 Pages: 197-210
  • NAID: 40017654623
  • Peer Reviewed
• [Journal Article] Distributions of simple patterns in some kinds of exchangeable sequences (2011)
  • Author(s): Kiyoshi Inoue, Sigeo Aki, Katuomi Hirano
  • Journal Title: Journal of Statistical Planning and Inference Volume: 141 Issue: 8 Pages: 2532-2544
  • DOI: 10.1016/j.jspi.2011.02.002
  • Peer Reviewed
• [Journal Article] Bivariate Fibonacci polynomials of order k with statistical applications (2011)
  • Author(s): K.Inoue, S.Aki
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 63 Pages: 197-210
  • NAID: 40017654623
  • Peer Reviewed
• [Presentation] クーポンコレクター問題と統計的推測 (2014)
  • Author(s): 安芸重雄, 平野勝臣
  • Organizer: 日本数学会2014年度年会
  • Place of Presentation: 学習院大学(東京都)
  • Year and Date: 2014-03-17
• [Presentation] 非サイクル有向グラフ上の連,スキャンの分布 (2014)
  • Author(s): 井上潔司, 安芸重雄
  • Organizer: 日本数学会2014年度年会
  • Place of Presentation: 学習院大学(東京都)
  • Year and Date: 2014-03-17
• [Presentation] 向きのないグラフィカルモデル上の離散パターンの数の分布 (2013)
  • Author(s): 安芸重雄, 井上潔司
  • Organizer: 日本数学会2013年度年会
  • Place of Presentation: 京都大学(京都府)
  • Year and Date: 2013-03-21
• [Presentation] Distributions of simple patterns in some kinds of exchangeable sequences (2012)
  • Author(s): 井上潔司, 安芸重雄, 平野勝臣
  • Organizer: 2012年度統計関連学会連合大会
  • Place of Presentation: 北海道大学(北海道)
  • Year and Date: 2012-09-11
• [Presentation] Exchangeable sequencesに基づいた離散分布モデルと統計的推測 (2012)
  • Author(s): 安芸重雄
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学(東京都)
  • Year and Date: 2012-03-28
• [Presentation] Exchangeable sequenceに基づいた離散分布モデルと統計的推測 (2012)
  • Author(s): 安芸重雄
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-28
• [Presentation] 可換試行列上の連の分布 (2011)
  • Author(s): 井上潔司, 安芸重雄
  • Organizer: 日本数学会2011年度年会
  • Place of Presentation: 早稲田大学(東京都)
  • Year and Date: 2011-03-22
• [Presentation] クーポンコレクター問題と統計的推測
  • Author(s): 安芸重雄，平野勝臣
  • Organizer: 日本数学会2014年度年会
  • Place of Presentation: 学習院大学（東京都）
• [Presentation] Distributions of simple patterns in some kinds of exchangeable sequences
  • Author(s): 井上潔司，安芸重雄，平野勝臣
  • Organizer: 2012年度統計関連学会連合大会
  • Place of Presentation: 北海道大学
• [Presentation] 向きのないグラフィカルモデル上の離散パターンの数の分布
  • Author(s): 安芸重雄，井上潔司
  • Organizer: 日本数学会2013年度年会
  • Place of Presentation: 京都大学