2013 Fiscal Year Final Research Report
A new development of Bayesian prediction using saddlepoint equalities
| Project/Area Number |
23500354
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Kyushu University |
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Principal Investigator |
OHNISHI Toshio 九州大学, 経済学研究科(研究院), 准教授 (60353413)
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| Co-Investigator(Renkei-kenkyūsha) |
YANAGIMOTO Takemi 中央大学, 理工学部, 客員教授 (40000195)
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| Research Collaborator |
DUNN Peter University of the Sunshine Coast, Australia
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| Project Period (FY) |
2011 – 2013
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| Keywords | 統計的推測 / Bayes統計学 / モデル平均 / 熱力学 / 情報量基準 / 凸関数 / Legendre変換 |
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| Research Abstract |
The likelihood maximization and the Shannon entropy maximization are two of the most fundamental principles in statistics. Focusing attention on a common mathematical structure between Bayesian prediction and thermodynamics, this research revealed a very interesting relationship, which should be called duality, between these two principles. Under a certain loss function the Shannon entropy maximization derives the best prediction while the likelihood maximizatiton leads to the worst prediction. Under a dual loss function the roles of these two principles are reversed, and the likelihood maximization derives the best prediction and the Shannon entropy maximization leads to the worst prediction.
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