| 抗差贝叶斯估计及应用 |
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| 引用本文： | 杨元喜.抗差贝叶斯估计及应用[J].测绘学报,1992,21(1):42-49. |
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| 作者姓名： | 杨元喜 |
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| 作者单位： | 郑州测绘学院 |
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| 摘 要： | 当未知参数具有先验期望和方差，且观测值与未知参数先验值均服从正态分布时，最小二乘贝叶斯估计将给出参数的最优解。然而当观测值和参数先验值的实际分布有悖于正态假设时，经典贝叶斯估计使估值偏高。本文基于常用的M估计原理，对三种类型的误差模式，导出了M－LS、LS－M和M－M三种抗差贝叶斯估计解式和影响函数；讨论了相应的计算方法；给出了参数验后方差表达式。
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| 关 键 词： | 抗差 贝叶斯估计 函数 方差 测量 |
ROBUST BAYESIAN ESTIMATION |
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| Yang Yuanxi.ROBUST BAYESIAN ESTIMATION[J].Acta Geodaetica et Cartographica Sinica,1992,21(1):42-49. |
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| Authors: | Yang Yuanxi |
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| Institution: | Zhengzhou Institute of Surveying and Mapping |
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| Abstract: | :
Bayesian estimation based on the assumption of multivariate Gaussian distributions are known to be nonrobust. This means that when the prior distribution of parameters and the distribution of the observations are not Gaussian, the estimators obtained from !Ba-y.esian method must heavily be influenced. In this article, three robust (M-LS, LS-M a.nd M-M) estimators for the three corresponding error models are described based -on the principle of M estimation. The influence functions of three robust Bayesian esti mations are given. The algorithm problems are discussed and the expressions for the posterior variance-covariance are derived. |
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| Keywords: | :Robuot Bayesian estimation Influence function Posterior variance-cov-ariance |
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