2005 Fiscal Year Final Research Report Summary
The Foundation of Mathematical Statistics on Quantum Inference and Its Applications
| Project/Area Number |
14204006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tsukuba |
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Principal Investigator |
AKAHIRA Masafumi University of Tsukuba, Graduate School of Pure and Applied Sciences, Professor, 大学院・数理物質科学研究科, 教授 (70017424)
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| Co-Investigator(Kenkyū-buntansha) |
AOSHIMA Makoto University of Tsukuba, Graduate School of Pure and Applied Sciences, Associate Professor, 大学院・数理物質科学研究科, 助教授 (90246679)
HAYASHI Masato University of Tokyo, Graduate School of Information Science and Technology, Associate Professor, 大学院・情報理工学研究科, 助教授 (40342836)
YAMATO Hajime Kagoshima University, Faculty of Science, Professor, 理学部, 教授 (90041227)
KAGEYAMA Sanpei Hiroshima University, Faculty of Education, Professor, 大学院・教育研究科, 教授 (70033892)
MAESONO Yoshihiko Kyushu University, Faculty of Economics, Professor, 大学院・経済学研究院, 教授 (30173701)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Quantum estimation / Quantum test / Quantum information geometry / Sequential analysis / Sequential estimation / Combinatorial theory / Experimental design / Quantum mechanics |
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| Research Abstract |
The statistical investigation on various themes was done as follows. (1) Involving a relationship between statistical models and statistics, the properties of the models were discussed and some interesting results on the behavior of various statistics are obtained. (2) In the theory of statistics to finance, time series and their applications, statistical procedures were shown to be asymptotically useful. (3) In the experimental design and its related area, the mathematical structure is clarified by combinatorial procedures, and results intended to apply to practical problems were obtained. (4) In statistical sequential inference, some sequential procedures were proposed, and their properties were discussed in details. The asymptotic efficiencies were shown. (5) The construction of mathematically fundamental theory of biostatistics is tried, and statistically inferential procedures are shown to play an important role. In particular, bioassay test, score test etc. were shown to be usefu
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l. (6) The relationship between non-locality in quantum mechanics and statistical inference is clarified, and inferential procedures is also shown to be efficient in quantum estimation and quantum test. Further, it is recognized to play an important role as the theoretical base of concrete physical phenomena. (7) In statistical inference, on the lower bound for tail probabilites of consistent estimators, the first and second order asymptotic efficiencies are investigated from a different viewpoint from conventional Bahadur efficiency. And in order to unify both of non-parametric and parametric tests, the mathematical setup was done, new test statistics based on estimators of spectral density matrics were proposed, and their asymptotic properties are derived. (8) Under a family of non-parametric quantum states, state estimation, prediction of quantum state, quantum information geometry and discrimination problem on quantum states are trated, and new interesting results were obtained. Many symposium on the above were held and active discussion and mutual exchange of information were also done. Their results were summarized as a volume. Less
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Research Products
(14 results)
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[Book] 特異モデルの統計学2004
Author(s)
福水健次, 栗木哲, 竹内啓, 赤平昌文
Total Pages
ix+274
Publisher
岩波書店
Description
「研究成果報告書概要(和文)」より
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