2010 Fiscal Year Final Research Report
Theory of the foundation of mathematical statistics to analyze the biological information and its applications
| Project/Area Number |
19340020
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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, 副学長 (70017424)
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| Co-Investigator(Kenkyū-buntansha) |
AOSHIMA Makoto 筑波大学, 大学院・数理物質科学研究科, 教授 (90246679)
KOIKE Kenーichi 筑波大学, 大学院・数理物質科学研究科, 准教授 (90260471)
OHYAUCHI Nao 筑波大学, 大学院・数理物質科学研究科, 助教 (40375374)
TORIGOE Norio 東海大学, 理学部, 准教授 (40297180)
SHIRAISHI Takaaki 南山大学, 情報理工学部, 教授 (50143160)
TANAKA Hidekazu 大阪府立大学, 大学院・工学研究科, 講師 (50302344)
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| Co-Investigator(Renkei-kenkyūsha) |
KONNO Yoshihiko 日本女子大学, 理学部, 教授 (00205577)
KUBOKAWA Tatsuya 東京大学, 大学院・経済学研究科, 教授 (20195499)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 生物統計 / 臨床統計 / 情報量 / 漸近有効性 / 一致性 / 非心分布 / Bernoulli分布 / Cornish-Fisher展開 |
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| Research Abstract |
The research on basic theory of statistical mathematics in the information analysis of bioinformatics, medical sciences, etc. In particular, we consider the problem on sequential experiment of choice, and develop a procedure which maximizes the expected effect in an application plan of 2 treatments in clinical trials. The statistic playing an important role in the inference of two-sample problem follows a non-central distribution in many cases. We analytically derive an approximation formula of a percentage point of the non-central chi-square distribution with the odd degree of freedom, and numerically evaluate the goodness of the approximation of the non-central distribution from the viewpoint of the power and the non-centrality. Further, we derive a higher order approximation formula of the percentage point of the non-central t-statistic, and numerically verify the accuracy of the formula under various distributions.
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