An Attempt to Developing the Hybrid Bayesian Conjugate Analysis
| Project/Area Number |
18500220
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Chuo University (2007)
The Institute of Statistical Mathematics (2006) |
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Principal Investigator |
YANAGIMOTO Takemi Chuo University, Faculty of Science and Engineering, Visiting Professor (40000195)
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| Co-Investigator(Kenkyū-buntansha) |
TOSHIO Ohnishi The Institute of Statistical Mathmatics, Department of Date Science, Assistant Professor (60353413)
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| Project Period (FY) |
2006 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥330,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
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| Keywords | Bavesian method / Generalized linear model / Predictive distribution / Coniueate nrior distribution / Comparison of estimators / Frequentist approach / Gaussian hyper-geometric function / ガウス超幾何関数 / ベイズ法 / 共通母数の推定 / 修正尤度法 / 特殊関数 / 高次元母数の推定 |
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| Research Abstract |
The aim of the present research is to allow Bayesian methods to be acceptable for usual statistical users such as frequentists. It becomes now apparent that Bayesian methods are useful when the model employed contains a high-dimensional parameter This aspect is now important, since such a model is becoming popular in order to apply a realistic model explaining adequately characteristics of the data set in the study. Although a model having a high-dimensional parameter gave rise to serious problem pertaining to numerical computations, this burden is eliminated due to advances in numerical instruments and techniques.
Our approach is to assume a prior distribution only on a part of parameters. This is because a part ofparameters are subject to controversy, and it is not easy to assume a prior distribution acceptable for both sides of stakeholders. When the portion is relatively small, we can expect both advantages of Bayesian and frequentist approaches, since we assume a prior distribution
… More
on a high-dimensional parameter but do not assume a prior distribution on parameters under controversy. This approach gives rises to various interesting problems to be solved. An example is to reduce necessary computations in terms of the special functions. Note that the use of special functions can allow us the analytical evaluation of the functions appeared in the analysis. Actual models in the study contain the generalized linear model with multiple strata containing a common slope parameter through strata where an error distribution is in the exponential family. A primary interest in this model is usually placed on the common slope parameter, and the remaining stratum-wise parameters are.of secondary interest Recall that such parameter was often treated as nuisance. Such a treatment, however is unrealistic but was employed because of avoidable technical reasons. The present research showed that our research program meets with the need of the current theoretical statistics. We succeeded in proposing several practical methods for inference of a common parameter through strata. The actual error distributions cover the gamma and binomial distributions, which are familiar in the practical data analysis
As a byproduct of our research program we obtained an unexpected result, though any result is not published as yet. It pertains to the relation between the test statistic and the predictive density. It looks that the close relation is widely accepted among theoretical researchers, but any explicit test statistic is no proposed. Note that further detailed studies will be necessary to implement a test statistic and a confidence interval. Less
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Research Products
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