非线形模型方差的贝叶斯估计(英文)

Bayesian estimation of variance factorin the nonlinear model

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.

<Abstrcat>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.