Reconstructing the empirical Bayes method through the use of the posterior density
| Project/Area Number |
23500357
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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 | Chuo University |
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Principal Investigator |
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| Co-Investigator(Renkei-kenkyūsha) |
OHNISHI Toshio 九州大学, 経済学研究科, 准教授 (60353413)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | Bayes 法 / 事後密度 / 退化型事前分布 / 凸関数 / 予測子 / DIC / ベイズ法 / 弱い事前密度 / 無情報事前密度 / 経験ベイス法 / 分布の裾の重さ / 交叉検証法 / 平滑化 / ２x２分割表 |
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| Research Abstract |
An unknown hyperparameter is contained in a prior density in the empirical Bayes method. Our primary aim is placed on attempting to evaluate a prior density in terms of a posterior density. We developed the empirical Bayes methods applicable to a wide variety of prior densities. Emphasis is placed on the flexible use of a prior density containing only limited amount of information. Amount of information contained in a prior density is represented through the heaviness of concentration of the density about a fixed point. For this purpose we rigidly define a novel notion of the heaviness of concentration. Further, a likelihood of a Bayesian model based on a mixture of sampling density is introduced. It may be surprising that any formal definition of such a likelihood is not found at all in existing literature. At the final stage of the present research it becomes apparent that our approach is applicable to an important problem of combining evidences from different sources.
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Report
(4 results)
Research Products
(53 results)
