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Concepts and Roles of Information in Statistics

Research Project

Project/Area Number 61450073
Research Category

Grant-in-Aid for General Scientific Research (B)

Allocation TypeSingle-year Grants
Research Field 統計学
Research InstitutionThe Institute of Statistical Mathematics

Principal Investigator

MATSUNAWA Tadashi  The Institute of Statistical Mathematics, 統計基礎研究系, 教授 (40036041)

Co-Investigator(Kenkyū-buntansha) KASHIWAGI Nobuhisa  The Institute of Statistical Mathematics, 調査実験解析研究系, 助手 (50150032)
KUBOKI Hisataka  The University of Electro-Communications, 電気通信学部, 助教授 (10132698)
BABA Yasumasa  The Institute of Statistical Mathematics, 調査実験解析研究系, 助教授 (90000215)
MURAKAMI Masakatsu  The Institute of Statistical Mathematics, 統計教育情報センター, 助教授 (00000216)
Project Period (FY) 1986 – 1987
Project Status Completed (Fiscal Year 1987)
Budget Amount *help
¥4,900,000 (Direct Cost: ¥4,900,000)
Fiscal Year 1987: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1986: ¥3,400,000 (Direct Cost: ¥3,400,000)
KeywordsInformation / Entropy / Graphical Representation of Statistical Information / Separate Inference / セパレート推論 / ベイズ手法 / 修正情報量基準
Research Abstract

The objectives of this project are to investigate and make clear concepts and roles of "information" in statistics from various points of view. Emphasis of the investigation was put on five items and results were obtained with fairy good success:
1. Fundamental concepts of information: The concepts of Kullback's information number and entropy were considered through the thermodynamic background and Boltzmann-Plancks' principle. It was also pointed out that Planck's approach to get his radiation formula contained useful results even to modern statistical theory.
2. Information and separate inference: A basis for a unified approach to the theory of measures of information in separate inference was discussed on the basis of the concept of smoothness of a statistical model.
3. Bayes method and information: Two likelihood functions were deduced from a combination of linear models. One is usual likelihood function and another is Bayesian likelihood one. A proof that these likelihood functions are equivalent was presented.
4. Graphical representation of information: Graphical method for the problem concerned with qualitative or categorical data was shown. Among various graphical methods for representing multivariate data, constellation graph was shown to be appropriate to represent response patterns and to make prediction based on categorical data.
5. Decision and information: A statistical decision theoretic approach was proposed to give the optimal number of sensors in certain structure of sensor systems. Some numerical examples were also presented.

Report

(2 results)
  • 1987 Final Research Report Summary
  • 1986 Annual Research Report
  • Research Products

    (17 results)

All Other

All Publications (17 results)

  • [Publications] T. Matsunawa: Annals of the Institute of Statistical Mathematics. 38. 205-222 (1986)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Y. Baba: Computational Statistics and Data Analysis. 5. 85-101 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] H. Kuboki: Annals of the Institute of Statistical Mathematics. 39. 1-23 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] N. Kashiwagi: Research Memorandum No. 326, Inst. Statist. Math.1-12 (1987)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] T. Matsunawa: Research Memorandum No. 344, Inst. Statist. Math.1-58 (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] H. Kuboki: Proceedings of the 2nd Pacific Area Statistical Conference. (1988)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] T. Matsunawa: "Modified Information Criteria for a Uniform Approximate Equivalence of Probability Distributions" Annals of the Institute of Statistical Mathematics. 38. 205-222 (1986)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] Y. Baba: "Graphical Prediction Method based on Categorical Data" Computational Statistics and Data Analysis. 5. 85-101 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] H. Kuboki: "Analysis of Marginal and Conditional Density Functions for Separate Inference" Annals of the Institute of Statistical Mathematics. 39. 1-23 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] N. Kashiwagi: "A Relation Between two likelihood Functions Deduced from a Bombination of Linear Models" Research Memorandum No. 326, Inst. Statist. Math.1-12 (1987)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] T. Matsunawa: "Entropy and Statistical Information" Research Memorandum No. 344, Inst. Statist. Math.1-58 (1988)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1987 Final Research Report Summary
  • [Publications] T.Matsunawa: Annals of the Institute of Statistical Mathematics. 38. 205-222 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] Y.Baba: Proceedings of the 2nd Japan-China Symposium on Statistics. 17-20 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] N.Kashiwagi: Proceedings of the Institute of Statistical Mathematics. 34. 215-222 (1986)

    • Related Report
      1986 Annual Research Report
  • [Publications] H.Kuboki: Annals of the Institute of Statistical Mathematics. 39. 1-23 (1987)

    • Related Report
      1986 Annual Research Report
  • [Publications] T.Matsunawa: Report in Scientific Research. 1-67 (1988)

    • Related Report
      1986 Annual Research Report
  • [Publications] H.Kuboki: Proceedings of the 2nd Pacific Area Statistical Conference. (1988)

    • Related Report
      1986 Annual Research Report

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Published: 1987-03-31   Modified: 2016-04-21  

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