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A new approach to design of experiments by computational algebraic methods

Research Project

Project/Area Number 17K00048
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Statistical science
Research InstitutionKobe University

Principal Investigator

AOKI Satoshi  神戸大学, 理学研究科, 教授 (90332618)

Project Period (FY) 2017-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywords計算代数 / 実験計画法 / グレブナー基底 / イデアル / 直交計画 / 一部実施計画 / 指示関数 / 素イデアル分解 / 多項式環 / 準素イデアル分解 / ANOVAモデル / 計算代数統計 / 最適計画 / マルコフ基底
Outline of Final Research Achievements

The aim of this research is to formulate problems related to the theory of experimental design for several multi-level factors using computational algebraic techniques and obtain new results. The most important result during this research period is the establishment of a methodology for characterizing fractional factorial designs as zeros of polynomial ideals. Based on this result, for several problems that are considered important in applications, new results were obtained by defining ideals of polynomial rings corresponding to fractional factorial designs with given characteristics, enumerating their zeros using computational algebraic techniques, and further classifying them into equivalence classes.

Academic Significance and Societal Importance of the Research Achievements

本研究課題で取り組んだ実験計画法は、応用統計学の重要な一分野である。実験計画法の理論は、数理統計学の研究者だけでなく、広く現場の技術者に理解されるべきものである、という側面がある。そのため、従来の実験計画法の研究は、普及を念頭に置いた、分かりやすい理論構築や使い方の整備が重視されてきた側面があり、一方で、一般的な設定における理論の整備などの数学的な研究が、不十分な面があったといえる。本研究で考えた多水準因子の実験計画も、従来は2水準や3水準因子についての使いやすい手法の整備が重視されていた。それに対し本研究では、完全に一般的な設定でいくつかの結果を得ることに成功した。

Report

(8 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • Research Products

    (32 results)

All 2024 2023 2022 2021 2020 2019 2018 2017

All Journal Article (7 results) (of which Peer Reviewed: 6 results,  Open Access: 1 results) Presentation (19 results) (of which Int'l Joint Research: 2 results,  Invited: 6 results) Book (5 results) Funded Workshop (1 results)

  • [Journal Article] 直積構造をもたない内側・外側配置2023

    • Author(s)
      青木敏、野呂正行
    • Journal Title

      品質

      Volume: 53 Pages: 64-73

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Use of indicator functions to enumerate cross-array designs without direct product structure2023

    • Author(s)
      Satoshi Aoki, Masayuki Noro
    • Journal Title

      Algebraic Statistics

      Volume: 14

    • Related Report
      2023 Annual Research Report
  • [Journal Article] Use of primary decomposition of polynomial ideals arising from indicator functions to enumerate orthogonal fractions2022

    • Author(s)
      Aoki Satoshi、Noro Masayuki
    • Journal Title

      Japanese Journal of Statistics and Data Science

      Volume: - Issue: 1 Pages: 165-179

    • DOI

      10.1007/s42081-022-00149-z

    • Related Report
      2022 Research-status Report 2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Carbon-Carbon Bond Formation between N-Heterocyclic Carbene Ligand on Ruthenium Carbene Catalysts and 1,4-Naphthoquinone via Intramolecular Carbon(sp3)-Hydrogen Bond Activation2021

    • Author(s)
      Wada Yuki、Takehara Tsunayoshi、Suzuki Takeyuki、Aoki Satoshi、Hibi Takayuki、Sako Makoto、Tsujino Hirofumi、Tsutsumi Yasuo、Arisawa Mitsuhiro
    • Journal Title

      Organometallics

      Volume: 40 Issue: 16 Pages: 2901-2908

    • DOI

      10.1021/acs.organomet.1c00350

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] 計画上の分散分析モデルと多項式モデル2020

    • Author(s)
      今井大樹,青木敏
    • Journal Title

      応用統計学

      Volume: 49

    • NAID

      130008022514

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterizations of indicator functions and contrast representations of fractional factorial designs with multi-level factors2019

    • Author(s)
      Satoshi Aoki
    • Journal Title

      Journal of Statistical Planning and Inference

      Volume: 203 Pages: 91-105

    • DOI

      10.1016/j.jspi.2019.03.003

    • Related Report
      2019 Research-status Report 2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Markov bases for two-way change-point models of ladder determinantal tables2017

    • Author(s)
      Satoshi Aoki and Takayuki Hibi
    • Journal Title

      Journal of Algebraic Statistics

      Volume: 8 Issue: 1

    • DOI

      10.18409/jas.v8i1.55

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] 代数手法による一部実施計画の列挙2024

    • Author(s)
      青木敏
    • Organizer
      九州大学統計科学セミナー
    • Related Report
      2023 Annual Research Report
  • [Presentation] 非直積型配置による統計解析2023

    • Author(s)
      青木敏, 野呂正行
    • Organizer
      日本品質管理学会 第131回研究発表会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 実験計画・分割表・グレブナー基底2023

    • Author(s)
      青木敏
    • Organizer
      統計関連学会連合大会
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] 非直積型配置による統計解析2023

    • Author(s)
      青木敏, 野呂正行
    • Organizer
      統計関連学会連合大会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 非直積型計画を利用した望目特性のパラメータ設計2023

    • Author(s)
      青木敏
    • Organizer
      第120回テクノメトリックス研究会
    • Related Report
      2023 Annual Research Report
  • [Presentation] 非直積型配置による統計解析2023

    • Author(s)
      青木敏、野呂正行
    • Organizer
      日本品質管理学会 第131回研究発表会
    • Related Report
      2022 Research-status Report
  • [Presentation] 直積構造をもたない内側・外側配置2022

    • Author(s)
      青木敏、野呂正行
    • Organizer
      確率・統計・行列ワークショップ
    • Related Report
      2022 Research-status Report
  • [Presentation] マルコフ連鎖モンテカルロ法のための計算代数2022

    • Author(s)
      青木敏
    • Organizer
      組合せ遷移 第26回セミナー
    • Related Report
      2022 Research-status Report
  • [Presentation] 実験計画法と計算代数2022

    • Author(s)
      青木敏
    • Organizer
      Workshop: シミュレーションとモデリングのための計算代数2022
    • Related Report
      2021 Research-status Report
  • [Presentation] 素イデアル分解を利用した一部実施計画の分類2021

    • Author(s)
      青木敏、野呂正行
    • Organizer
      2021年度統計関連学会連合大会
    • Related Report
      2021 Research-status Report
  • [Presentation] 計画上の分散分析モデルと多項式モデル2020

    • Author(s)
      青木敏
    • Organizer
      2020年度統計関連学会連合大会
    • Related Report
      2020 Research-status Report
  • [Presentation] Characterizations of indicator functions of fractional factorial designs2019

    • Author(s)
      青木敏
    • Organizer
      MACS SG4 & 11 Joint Seminar, 数学と統計・データ科学
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Algebraic methods in the design of experiments2019

    • Author(s)
      Satoshi Aoki
    • Organizer
      ISSAC 2019, The 44th International Symposium on Symbolic & Algebraic Computation. Beihang University, Beijing, China.
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Characterizations of indicator functions of fractional factorial designs2019

    • Author(s)
      青木敏
    • Organizer
      MACS SG4 & 11 Joint Seminar: 数学と統計・データ科学
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Characterizations of indicator functions for fractional factorial designs2018

    • Author(s)
      青木敏
    • Organizer
      統計関連学会連合大会
    • Related Report
      2018 Research-status Report
  • [Presentation] Characterizations of indicator functions of fractional factorial designs2018

    • Author(s)
      青木敏
    • Organizer
      実験計画法ならびに情報数理と関連する組合せ構造2018
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Characterizations of indicator functions of fractional factorial designs2018

    • Author(s)
      青木敏
    • 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] Characterizations of indicator functions of fractional factorial designs2018

    • Author(s)
      Satoshi Aoki
    • Organizer
      Computational and Methodological Statistics
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] 分配束に付随するイデアルのグレブナー基底と統計モデル2017

    • Author(s)
      青木敏、日比孝之
    • Organizer
      統計関連学会連合大会
    • Related Report
      2017 Research-status Report
  • [Book] 代数的統計モデル、理論統計学教程・数理統計の枠組み2019

    • Author(s)
      青木敏、竹村彰通、原尚幸
    • Total Pages
      272
    • Publisher
      共立出版
    • ISBN
      9784320113534
    • Related Report
      2019 Research-status Report
  • [Book] 計算代数統計 --- グレブナー基底と実験計画法 ---2018

    • Author(s)
      青木敏
    • Total Pages
      168
    • Publisher
      共立出版
    • ISBN
      9784320112605
    • Related Report
      2018 Research-status Report
  • [Book] 分割表の統計解析 --- 二元表から多元表まで ---2018

    • Author(s)
      宮川雅巳、青木敏
    • Total Pages
      145
    • Publisher
      朝倉書店
    • ISBN
      9784254128390
    • Related Report
      2018 Research-status Report
  • [Book] 確率・統計II2018

    • Author(s)
      青木敏、竹村彰通
    • Total Pages
      166
    • Publisher
      丸善出版
    • ISBN
      9784621302705
    • Related Report
      2018 Research-status Report
  • [Book] 東京大学工学教程、確率・統計II2018

    • Author(s)
      青木敏、竹村彰通
    • Total Pages
      166
    • Publisher
      丸善出版
    • ISBN
      9784621302705
    • Related Report
      2017 Research-status Report
  • [Funded Workshop] Current topics on algebraic statistics and related fields2018

    • Related Report
      2017 Research-status Report

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Published: 2017-04-28   Modified: 2025-01-30  

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