Concepts and Roles of Information in Statistics
| Project/Area Number |
61450073
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
統計学
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
MATSUNAWA Tadashi The Institute of Statistical Mathematics, 統計基礎研究系, 教授 (40036041)
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| 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)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| 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)
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| Keywords | Information / 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 |
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| 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.
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Report
(2 results)
Research Products
(17 results)
