2010 Fiscal Year Final Research Report
Construction methods for predictive distributions under multiplicity
| Project/Area Number |
20300097
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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 |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
KOMAKI Fumiyasu The University of Tokyo, 大学院・情報理工学系研究科, 教授 (70242039)
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| Co-Investigator(Renkei-kenkyūsha) |
OOHAMA Yasutada 徳島大学, 大学院・ソシオテクノサイエンス研究部, 教授 (20243892)
MOROHOSI Hozumi 政策研究大学院大学, 大学院・政策研究科, 教授 (10272387)
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| Project Period (FY) |
2008 – 2010
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| Keywords | ベイズ統計 / 情報量 |
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| Research Abstract |
It has been proved that priors maximizing the mutual information between the parameter and the quantity to be predicted given the observation play an essential role. By using this fact, prediction problems with multiplicity have been studied. It has been shown that predictive distributions resolving the multiplicity can be constructed as Bayesian predicitive distributions. The best prior distributions become complex and diffcult to obtain. Numerical approximation methods have been developed. In addition to binomial and multinomial models, prediction problems concerning linear regression models, time series models, and Wishart models have been investigated. Information geometrical properties of these models have been studied and applied to construct superior prediction.
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