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Development of the methods of statistical analysis for spatial data of Voronoi tessellation through MCMC method

Research Project

Project/Area Number 20500264
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

TANEMURA Masaharu  The Institute of Statistical Mathematics, 名誉教授 (80000214)

Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Keywordsボロノイ多角形 / 空間統計学 / 相互作用ポテンシャル / Gibbs分布 / 疑似尤度 / MCMC法 / モデル化 / 疑似尤度法 / ボロノイ多角形分割 / ランゲルハンス細胞 / 相互作用モデル / ギブス分布 / 近似尤度 / Gibbs点過程 / 擬似尤度 / 規格化因子
Research Abstract

It is known that there are many polygonal tessellation data in the field of natural sciences. But most of such data remained untouched from the point of statistical analysis. In order to break this situation, we have developed a statistical procedures using MCMC method in depth. As a result of our research, it is revealed that various types of polygonal tessellation pattern are reproducible in our statistical model and that statistical estimation of model parameters is able to execute.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (26 results)

All 2010 2009 2008 Other

All Journal Article (14 results) (of which Peer Reviewed: 8 results) Presentation (11 results) Remarks (1 results)

  • [Journal Article] 多角形分割データに対するMCMCによる統計モデルII2010

    • Author(s)
      種村正美
    • Journal Title

      2010年度統計関連学会連合大会報告集

      Pages: 120-120

    • Related Report
      2010 Final Research Report
  • [Journal Article] ボロノイ・セル相互作用モデルによる多角形分割パターンの解析2010

    • Author(s)
      種村正美
    • Journal Title

      形の科学会誌 25巻

      Pages: 200-201

    • NAID

      10027444670

    • Related Report
      2010 Final Research Report
  • [Journal Article] 多角形分割データに対するMCMCによる統計モデルII2010

    • Author(s)
      種村正美
    • Journal Title

      2010年度統計関連学会連合大会予稿集

      Pages: 278-278

    • Related Report
      2010 Annual Research Report
  • [Journal Article] ボロノイ・セル相互作用モデルによる多角形分割パターンの解析2010

    • Author(s)
      種村正美
    • Journal Title

      形の科学会誌

      Volume: 25 Pages: 200-201

    • NAID

      10027444670

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Spatial statistics for epidermal Langerhans cells Effects of protopic ointment 0.1% on spatial distribution--2009

    • Author(s)
      Numahara T., Tanemura, M, Numahara K., Moriue J., Shirahige Y., Yokoi I., Kubota Y.
    • Journal Title

      Forma Vol.24, No.1

      Pages: 49-59

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spatial statistics for epidermal Langerhans cells2009

    • Author(s)
      T.Numahara
    • Journal Title

      Forma 24

      Pages: 49-59

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Two different mechanisms of planar cell intercalation leading to tissue elongation2008

    • Author(s)
      Honda H., Nagai T., Tanemura, M.
    • Journal Title

      Developmental Dynamics Vol.237

      Pages: 1826-1836

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Computer simulation of emerging asymmetry in the mouse blastocyst2008

    • Author(s)
      Honda H., Motosugi N., Nagai T., Tanemura, M., Hiiragi T.
    • Journal Title

      Development Vol.135

      Pages: 1407-1414

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Voronoi adjustment model on 2-sphere for small number of points2008

    • Author(s)
      種村正美
    • Journal Title

      Proceedings of International Workshop VORONOI-2008

      Pages: 174-181

    • Related Report
      2010 Final Research Report
  • [Journal Article] Voronoi tilings for the Clifford torus in a 3-sphere2008

    • Author(s)
      Dolbilin N., Tanemura, M.
    • Journal Title

      Voronoi's Impact on Modern Science Book 4

      Pages: 210-219

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Two different mechanisms of planar cell intercalation leading to tissue elongation2008

    • Author(s)
      H. Honda
    • Journal Title

      Developmental Dynamics 237

      Pages: 1826-1836

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Computer simulation of emerging asymmetry in the mouse blastocyst2008

    • Author(s)
      H. Honda
    • Journal Title

      Development 135

      Pages: 1407-1414

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Voronoi adjustment model on 2-sphere for small number of points2008

    • Author(s)
      M. Tanemura
    • Journal Title

      Proceedings of the Int. Workshop VORONOI-2008

      Pages: 174-181

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Voronoi tilings for the Clifford torus in a 3-sphere2008

    • Author(s)
      N. Dolbilin
    • Journal Title

      Voronoi's Impact on Modern Science Book4

      Pages: 210-219

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] ボロノイ・セル相互作用モデルによる多角形分割パターンの解析2010

    • Author(s)
      種村正美
    • Organizer
      第70回形の科学シンポジウム
    • Place of Presentation
      兵庫県立加古川東高等学校
    • Year and Date
      2010-11-21
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] 多角形分割データに対するMCMCによる統計モデルII2010

    • Author(s)
      種村正美
    • Organizer
      2010年度統計関連学会連合大会
    • Place of Presentation
      早稲田大学
    • Year and Date
      2010-09-07
    • Related Report
      2010 Annual Research Report 2010 Final Research Report
  • [Presentation] Mathematica Nearest Functionと点配置パターン解析2009

    • Author(s)
      沼原利彦
    • Organizer
      第68回形の科学シンポジウム
    • Place of Presentation
      栃木県下都賀郡壬生町
    • Year and Date
      2009-11-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] 多角形分割データに対するMCMCによる統計モデル2009

    • Author(s)
      種村正美
    • Organizer
      2009年度統計関連学会連合大会
    • Place of Presentation
      同志社大学(京田辺市)
    • Year and Date
      2009-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] 多角形分割データに対するMCMCによる統計モデル2009

    • Author(s)
      種村正美
    • Organizer
      2009年度統計関連学会連合大会
    • Place of Presentation
      京田辺市
    • Year and Date
      2009-09-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Optimal configuration on 2-sphere for small number of points2009

    • Author(s)
      種村正美
    • Organizer
      ISM Symposium on Stochastic Models and Discrete Geometry
    • Place of Presentation
      統計数理研究所
    • Year and Date
      2009-02-19
    • Related Report
      2010 Final Research Report
  • [Presentation] Optimal configuration on 2-sphere for small number of points2009

    • Author(s)
      M. Tanemura
    • Organizer
      ISM Symposium on Stochastic Models and Discrete Geometry
    • Place of Presentation
      統計数理研究所、東京
    • Year and Date
      2009-02-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] Voronoi tilings for the Clifford torus in a 3-sphere2008

    • Author(s)
      種村正美
    • Organizer
      4^<th> Int.Conf.on Analytic Number Theory and Spatial Tessellations
    • Place of Presentation
      キエフ(ウクライナ)
    • Year and Date
      2008-09-25
    • Related Report
      2010 Final Research Report
  • [Presentation] Voronoi tilings for the Clifford torus in a 3-sphere2008

    • Author(s)
      M. Tanemura
    • Organizer
      4th International Conf. on Analytic Num. Theory, Spatial Tessellations
    • Place of Presentation
      Drahomanov Nat. Pedag. Univ., Kyiv, Ukraine
    • Year and Date
      2008-09-25
    • Related Report
      2008 Annual Research Report
  • [Presentation] Voronoi adjustment model on 2-sphere for small number of points2008

    • Author(s)
      種村正美
    • Organizer
      International Workshop VORONOI-2008
    • Place of Presentation
      モスクワ(ロシア)
    • Year and Date
      2008-06-12
    • Related Report
      2010 Final Research Report
  • [Presentation] Voronoi adjustment model on 2-sphere for small number of points2008

    • Author(s)
      M. Tanemura
    • Organizer
      International Workshop VORONOI-2008
    • Place of Presentation
      Computing Center, RAS, Moscow, Russia
    • Year and Date
      2008-06-12
    • Related Report
      2008 Annual Research Report
  • [Remarks] ホームページ等

    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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