• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2013 Fiscal Year Final Research Report

Statistical inference on discrete patterns on random structures

Research Project

  • PDF
Project/Area Number 22540159
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKansai 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
Keywords統計数学
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

    (13 results)

All 2014 2013 2012 2011

All Journal Article (7 results) (of which Peer Reviewed: 7 results) Presentation (6 results)

  • [Journal Article] Coupon collector's problems with statistical applications to rankings2013

    • Author(s)
      Aki, S. and Hirano, K.
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.65 Pages: 571-587

    • DOI

      10.1007/s10463-012-0382-9

    • Peer Reviewed
  • [Journal Article] Distributions of numbers of runs and scans on directed acyclic graphs with generation2013

    • Author(s)
      Inoue, K. and Aki, S.
    • Journal Title

      Computational Statistics

      Volume: Vol.28 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 graphs2013

    • Author(s)
      Inoue, K., Aki, S., and Balakrishnan, N.
    • Journal Title

      Methodology and Computing in Applied Probability

      Volume: Vol.15 Pages: 349-362

    • DOI

      10.1007/s11009-011-9246-7

    • Peer Reviewed
  • [Journal Article] Statistical modeling for discrete patterns in a sequence of exchangeable trials2012

    • Author(s)
      Aki, S.
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.64 Pages: 633-655

    • DOI

      10.1007/s10463-011-0325-x

    • Peer Reviewed
  • [Journal Article] Exact distributions of the number of pattern occurrences in undirected graphical models2012

    • Author(s)
      Aki, S. and Inoue, K.
    • Volume
      Vol.42
    • Pages
      59-79
    • URL

      http://www.terrapub.co.jp/journals/jjss/frame/42.html

    • Peer Reviewed
  • [Journal Article] Bivariate Fibonacci polynomials of order k with statistical applications2011

    • Author(s)
      Inoue, K. and Aki, S.
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.63 Pages: 197-210

    • DOI

      10:1007/s10463-008-0217-x

    • Peer Reviewed
  • [Journal Article] Distributions of simple patterns in some kinds of exchangeable sequences2011

    • Author(s)
      Inoue, K., Aki, S. and Hirano, K.
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: Vol.141 Pages: 2532-2544

    • DOI

      10.1016/j.jspi.2011.02.002

    • 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 sequences2012

    • 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] 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

URL: 

Published: 2015-07-16  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi