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Fast numerical computation for multivariate distributions with combinatorial structure and its application to spatial epidemiology

Research Project

Project/Area Number 21500288
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Statistical science
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

KURIKI Satoshi  統計数理研究所, 数理・推論研究系, 教授 (90195545)

Co-Investigator(Renkei-kenkyūsha) TAKAHASHI Kunihiko  国立保健医療科学院, 技術評価部, 研究員 (50323259)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords空間疫学 / スキャン統計 / コーダルグラフ / 多重検定 / スキャン統計量
Research Abstract

In spatial epidemiology, it is important to evaluate the multiplicity-adjusted p-value of scan statistics by taking their spatial correlations into account. However, it is difficult to conduct exact numerical calculation because high-dimensional integrations are required. On the other hand, Monte Carlo simulations cannot yield precise results. In our proposed method, we represent the spatial correlations of scan statistics as a graph, and by extracting its Markov structure, rewrite the high-dimensional integration as a successive numerical integration. Although, the proposed method reduces computational time of integration drastically, it is not powerful enough for the real datasets. More research is needed for practical use.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (9 results)

All 2012 2011 2010 2009

All Journal Article (6 results) (of which Peer Reviewed: 4 results) Presentation (3 results)

  • [Journal Article] 2次多項式回帰曲線の正値性検定2012

    • Author(s)
      加藤直広、栗木哲
    • Journal Title

      応用統計学

      Volume: 41巻 Pages: 1-15

    • NAID

      10030592355

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] 2次多項式回帰曲線の正値性検定2012

    • Author(s)
      加藤直広
    • Journal Title

      応用統計学

      Volume: 41 Pages: 1-15

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Graph presentations for moments of noncentral Wishart distributions and their applications2010

    • Author(s)
      Satoshi Kuriki and Yasuhide Numata
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: Vol.62 Pages: 645-672

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Graph presentations for moments of noncentral Wishart distributions and their applications2010

    • Author(s)
      Satoshi Kuriki, Yasuhide Numata
    • Journal Title

      Annals of the Institute of Statistical Mathematics

      Volume: 62 Pages: 645-672

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Volume of tubes and the distribution of the maximum of a Gaussian random field, Selected Papers on Probability and Statistics2009

    • Author(s)
      Satoshi Kuriki, Akimichi Takemura
    • Journal Title

      American Mathematical Society Translations Series 2

      Volume: Vol.227 Pages: 25-28

    • Related Report
      2011 Final Research Report
  • [Journal Article] Volume of tubes and the distribution of the maximum of a Gaussian random field2009

    • Author(s)
      Satoshi Kuriki, Akimichi Takemura
    • Journal Title

      Selected Papers on Probability and Statistics, American Mathematical Society Translations Series 2 227

      Pages: 25-48

    • NAID

      130004558855

    • Related Report
      2009 Annual Research Report
  • [Presentation] 空間疫学のp値計算のための逐次計算2011

    • Author(s)
      栗木哲
    • Organizer
      「数理統計学の新たな展開」(科学研究費「計算代数手法に基づく数理統計学の展開」基盤研究(A)22240029による研究集会)
    • Place of Presentation
      つくば国際会議場
    • Year and Date
      2011-07-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Tube method--An integral-geometric approach to statistical distribution theory2010

    • Author(s)
      Satoshi Kuriki
    • Organizer
      GEOMETRY, TOPOLOGY, ALGEBRA and NUMBER THEORY, APPLICATIONS "dedicated to the 120th anniversary of Boris Delone
    • Place of Presentation
      Steklov Mathematical Institute, Moscow, Russia
    • Year and Date
      2010-08-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Tube method---An integral-geometric approach to statistical distribution theory2010

    • Author(s)
      Satoshi Kuriki
    • Organizer
      GEOMETRY, TOPOLOGY, ALGEBRA and NUMBER THEORY, APPLICATIONS" dedicated to the 120th anniversary of Boris Delone
    • Place of Presentation
      Steklov Mathematical Institute, Moscow, Russia
    • Year and Date
      2010-08-16
    • Related Report
      2010 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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