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Developing statistical models representing diversity

Research Project

Project/Area Number 18K13454
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 12040:Applied mathematics and statistics-related
Research InstitutionKyushu University (2020)
The University of Tokyo (2018-2019)

Principal Investigator

Tsukuda Koji  九州大学, 数理学研究院, 准教授 (30764972)

Project Period (FY) 2018-04-01 – 2021-03-31
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords統計モデル / 確率分割 / 確率過程 / 共分散行列 / 適合度検定 / 統計的漸近理論 / 無限次元空間における弱収束 / ランダム組み合わせ構造
Outline of Final Research Achievements

This project aims to study random partition models used for representing statistical diversities from the viewpoint of mathematical properties and develop a new random partition model. In particular, we investigated approximations and asymptotic evaluations associated with the Ewens sampling formula and the Pitman sampling formula. Moreover, we proposed a discrimination analysis method based on the Dirichlet-multinomial model.

Statistical inference for some related stochastic process models and multivariate models were also studied. We discussed and proposed goodness-of-fit tests and change-point tests for stochastic process models. We proposed high-dimensional tests for some typical models of covariance matrices.

Academic Significance and Societal Importance of the Research Achievements

ユーエンス抽出公式やピットマン抽出公式に従う確率分割の挙動をこれまでより正確に評価できるようになり,これらのモデルを応用する場合により詳細な議論が可能になると期待される.また,提案した判別分析法は多様性が高い集団を考える場合に特に有用である.関連するモデルについての研究で得られた成果は,それぞれが独自のアプローチで検定法を考えたものであり,他のモデルへの広がりも期待できる.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (20 results)

All 2021 2020 2019 2018

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Open Access: 2 results) Presentation (15 results) (of which Int'l Joint Research: 3 results,  Invited: 3 results)

  • [Journal Article] Error Bounds for the Normal Approximation to the Length of a Ewens Partition2020

    • Author(s)
      Koji Tsukuda
    • Journal Title

      Pioneering Works on Distribution Theory

      Volume: - Pages: 55-73

    • DOI

      10.1007/978-981-15-9663-6_3

    • ISBN
      9789811596629, 9789811596636
    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Weak convergence of marked empirical processes in a Hilbert space and its applications2020

    • Author(s)
      Tsukuda Koji、Nishiyama Yoichi
    • Journal Title

      Electronic Journal of Statistics

      Volume: 14 Issue: 2 Pages: 3914-3938

    • DOI

      10.1214/20-ejs1761

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bayesian approach to discriminant problems for count data with application to multilocus short tandem repeat dataset2020

    • Author(s)
      Koji Tsukuda, Shuhei Mano, Toshimichi Yamamoto
    • Journal Title

      Statistical Applications in Genetics and Molecular Biology

      Volume: - Issue: 2

    • DOI

      10.1515/sagmb-2018-0044

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] High-dimensional testing for proportional covariance matrices2019

    • Author(s)
      Koji Tsukuda, Shun Matsuura
    • Journal Title

      Journal of Multivariate Analysis

      Volume: 171 Pages: 412-420

    • DOI

      10.1016/j.jmva.2019.01.011

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] On Poisson approximations for the Ewens sampling formula when the mutation parameter grows with the sample size2019

    • Author(s)
      Koji Tsukuda
    • Journal Title

      The Annals of Applied Probability

      Volume: 29 Issue: 2 Pages: 1188-1232

    • DOI

      10.1214/18-aap1433

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Pitman 分割の長さの積率に対する漸近評価2021

    • Author(s)
      佃 康司
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 四つのウィシャート行列の積のトレースに関する高次元極限定理とその応用2020

    • Author(s)
      佃 康司, 松浦 峻
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Related Report
      2020 Annual Research Report
  • [Presentation] ウィシャート行列に関する高次元極限定理を用いた共通主成分性の仮説検定2020

    • Author(s)
      佃 康司, 松浦 峻
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] Pitman 分割の長さの積率に対する漸近評価2020

    • Author(s)
      佃 康司
    • Organizer
      研究集会「大規模データの公開におけるプライバシー保護の理論と応用」
    • Related Report
      2020 Annual Research Report
  • [Presentation] A change detection procedure for an ergodic diffusion process2019

    • Author(s)
      Koji Tsukuda
    • Organizer
      13th International Conference on Computational and Financial Econometrics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Ewens分割の長さに対する正規近似の誤差評価2019

    • Author(s)
      佃 康司
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Related Report
      2019 Research-status Report
  • [Presentation] Ewens分割の長さに対する正規近似の誤差評価2019

    • Author(s)
      佃 康司
    • Organizer
      2019年度統計関連学会連合大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Goodness-of-fit tests for Markovian processes based on marked empirical processes2019

    • Author(s)
      Koji Tsukuda, Yoichi Nishiyama
    • Organizer
      3rd International Conference on Econometrics and Statistics
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 高次元正規ベクトルの分散共分散行列の比例性に関する2標本検定2019

    • Author(s)
      佃 康司,松浦 峻
    • Organizer
      応用統計学会2019年度年会
    • Related Report
      2019 Research-status Report
  • [Presentation] マーク付き経験過程に基づくマルコフ過程の適合度検定2019

    • Author(s)
      佃 康司,西山 陽一
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Research-status Report
  • [Presentation] An error bound for the normal approximation to the length of a Ewens partition2019

    • Author(s)
      Koji Tsukuda
    • Organizer
      国際ワークショップ「Pioneering Workshop on Extreme Value and Distribution Theories in Honor of Professor Masaaki Sibuya」
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Poisson-Dirichlet分布に従う母集団からの標本が保持する情報量について2018

    • Author(s)
      佃 康司,間野 修平
    • Organizer
      日本数学会2018年度秋季総合分科会
    • Related Report
      2018 Research-status Report
  • [Presentation] Ewens分割の長さの正規近似について2018

    • Author(s)
      佃 康司
    • Organizer
      研究集会「公的大規模データの利用におけるプライバシー保護の理論と応用」
    • Related Report
      2018 Research-status Report
  • [Presentation] Ewens抽出公式に対する正規近似とポアソン近似2018

    • Author(s)
      佃 康司
    • Organizer
      科研費シンポジウム「融合する統計科学」
    • Related Report
      2018 Research-status Report
  • [Presentation] Ewens--Pitman抽出公式に関連したいくつかの話題について2018

    • Author(s)
      佃 康司
    • Organizer
      合同研究会「公的大規模データの利用におけるプライバシー保護の理論と応用」
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2022-01-27  

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