| 非线形模型方差的贝叶斯估计 |
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| 引用本文： | 王志忠,宋允全.非线形模型方差的贝叶斯估计[J].云南大学学报(自然科学版),2005,27(4):289-294. |
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| 作者姓名： | 王志忠 宋允全 |
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| 作者单位： | 中南大学,数学学院,湖南,长沙,410083 |
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| 基金项目： | This paper is supported by the National Natural Foundation of China(49774209). |
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| 摘 要： | 在均方误差的条件下,系统地研究了非线形模型方差的贝叶斯估计,提出了共轭和无先验信息的最佳贝叶斯估计和最佳无偏贝叶斯估计以及方差的最佳条件无偏贝叶斯估计.还提出了带有共轭和无先验信息的方差的极大后验估计,最后用一个简单的例子来说明上述结论的可行性.
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| 关 键 词： | 非线形模型 方差 最佳贝叶斯估计 极大后验估计 |
| 文章编号： | 0258-7971(2005)04-0289-05 |
| 修稿时间： | 2005年4月1日 |
Bayesian estimation of variance factor in the nonlinear model |
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| WANG Zhi-zhong,SONG Yun-quan.Bayesian estimation of variance factor in the nonlinear model[J].Journal of Yunnan University(Natural Sciences),2005,27(4):289-294. |
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| Authors: | WANG Zhi-zhong SONG Yun-quan |
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| Institution: | School of Mathematical Science, Central South University, Changsha 410083, China |
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| Abstract: | Motivated by the theory of Bayesian estimation of variance factor for the linear model.An attempt is made to establish a corresponding estimation theory for the nonlinear model.Under the principle of the minimization of the mean square error,the Bayesian estimation of variance factor for the nonlinear model is systematically studied.Best Bayesian estimation and best-unbiased Bayesian estimation of variance factor with conjugate and no informative priors are presented.The best conditionally unbiased Bayesian estimation of variance factor is developed.To compare with above estimations,the maximum posterior estimations of variance factor with conjugate and no informative priors are presented.Finally,a simple example is given to illuminate above feasibility. |
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| Keywords: | nonlinear model variance factor Bayesian estimate maximum posterior estimation |
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