Statistical distribution theory on graphs

• Project/Area Number: 24540141
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Seikei University
• Principal Investigator: INOUE Kiyoshi 成蹊大学, 経済学部, 教授 (10384653)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Project Status: Completed (Fiscal Year 2014)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2014: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
• Keywords: 離散分布論 / 数え上げ問題 / アルゴリズム / 離散分布理論 / 信頼性工学 / 統計的分布理論 / 統計的推測理論 / グラフ

Outline of Final Research Achievements

I considered the three topics:「Discrete distribution theory on undirected graphs」,「Distribution theory of discrete patterns on directed acyclic graphs」,「On dual relationships between discrete distributions on bivariate sequences」. I proposed the methods and algorithm for deriving the probability distribution exactly. The illustrative examples are also given in order to demonstrate the feasibility of the methods and algorithm. Furthermore, I presented these results at five conferences and I published five papers on the above topics.

Research Products

• [Journal Article] Distributions of numbers of runs and scans on higher order Markov directed acyclic graphs with generation (2015)
  • Author(s): Inoue, K.
  • Journal Title: Josai Mathematical Monographs Volume: 8 Pages: 3-16
  • NAID: 120005575962
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 確率・統計に登場する超幾何 (2014)
  • Author(s): 井上潔司、竹村彰通
  • Journal Title: 数学セミナー2014年3月号 Volume: 53 Pages: 19-23
• [Journal Article] On sooner and later waiting time distributions associated with simple patterns in a sequence of bivariate trials (2013)
  • Author(s): Inoue, K. and Aki, S.
  • Journal Title: Metrika Volume: Online First Issue: 7 Pages: 895-920
  • DOI: 10.1007/s00184-013-0478-0
  • 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] 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] Exact distributions of the number of pattern occurrences in undirected graphical models (2012)
  • Author(s): Aki, S. and Inoue, K.
  • Journal Title: Journal of the Japan Statistical Society Volume: Vol. 42 Pages: 59-79
  • NAID: 10030867431
  • Peer Reviewed
• [Presentation] Distributions of numbers of runs and scans on higher order Markov directed acyclic graphs with generation (2014)
  • Author(s): 井上 潔司
  • Organizer: ワークショップ「統計科学とその周辺」
  • Place of Presentation: 城西大学
  • Year and Date: 2014-12-07
• [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: 2014年度日本数学会
  • Place of Presentation: 学習院大学
• [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 (2013)
  • Author(s): 安芸重雄，井上潔司
  • Organizer: 2013年度日本数学会年会
  • Place of Presentation: 京都大学
• [Presentation] Distributions of simple patterns in some kinds of exchangeable sequences (2012)
  • Author(s): 井上潔司，安芸重雄
  • Organizer: 2012年 統計関連学会 連合大会
  • Place of Presentation: 北海道大学