云南大学学报（自然科学版）
雲南大學學報（自然科學版）
운남대학학보（자연과학판）
JOURNAL OF YUNNAN UNIVERSTY(NATURAL SCIENCES EDITION)
2005年
4期
289-293,356
,共6页
非线形模型%方差%最佳贝叶斯估计%极大后验估计
非線形模型%方差%最佳貝葉斯估計%極大後驗估計
비선형모형%방차%최가패협사고계%겁대후험고계
nonlinear model%variance factor%Bayesian estimate%maximum posterior estimation
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.
在均方誤差的條件下,繫統地研究瞭非線形模型方差的貝葉斯估計,提齣瞭共軛和無先驗信息的最佳貝葉斯估計和最佳無偏貝葉斯估計以及方差的最佳條件無偏貝葉斯估計.還提齣瞭帶有共軛和無先驗信息的方差的極大後驗估計,最後用一箇簡單的例子來說明上述結論的可行性.
재균방오차적조건하,계통지연구료비선형모형방차적패협사고계,제출료공액화무선험신식적최가패협사고계화최가무편패협사고계이급방차적최가조건무편패협사고계.환제출료대유공액화무선험신식적방차적겁대후험고계,최후용일개간단적례자래설명상술결론적가행성.
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.
