Bayes's theorem and the use of prior knowledge in regression analysis
Bayes's theorem and the use of prior knowledge in regression analysis
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贝叶斯定理和先验知识在回归分析中的运用
DOI：
10.1093/biomet/51.1-2.219
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发表时间：
1964
期刊：
影响因子：
2.7
通讯作者：
A. Zellner
中科院分区：
文献类型：
--
作者：
G. Tiao;A. Zellner
翻译后摘要：正态回归模型的分析整合先验信息的问题，采用贝叶斯方法。对Theil和Goldberger的“混合"估计进行了重新解释，并提出了一个假设。结果表明，后验分布的β采取的产品的多元正态分布和多元t分布的形式。什么可以被视为一个概括的费雪的工作问题作出推论时，样本是从两个正常的人口与共同的均值和不等方差获得。在这种情况下，它表明，后验分布的β是在两个多元t分布的产品的形式。
Abstract : A Bayesian approach to the problem of integration prior information into the analysis of the normal regression model was adopted. A reinterpretation of the ''mixed'' estimaticedure of Theil and Goldberger was provided with an assumption. It was shown that the posterior distribution of beta takes the form of a product of multivariate normal and multivariate t distributions. What may be regarded as a generalization of Fisher's work on the problem of making inferences when samples are drawn from two normal populations with common mean and unequal variances was obtained. In this case, it was shown that the posterior dis tribution of beta is in the form of the product of two multivariate t distributions.