A Bayes Approach for Combining Correlated Estimates
A Bayes Approach for Combining Correlated Estimates
复制标题
组合相关估计的贝叶斯方法
DOI：
10.1080/01621459.1965.10480816
复制
发表时间：
1965
影响因子：
3.7
通讯作者：
S. Geisser
中科院分区：
文献类型：
--
作者：
S. Geisser
本文给出了一个估计问题的Bayes解，该问题涉及一个来自多元正态总体的样本，该样本具有任意未知的协方差矩阵，但向量均值的分量是相等的。假设一个特定的未规范的先验密度是一个方便的表达式，用于显示先验无知，然后证明了这个共同的平均值的后验间隔可以基于学生的t分布。如果先验信息可以方便地用自然共轭先验密度表示，则后验间隔也将取决于Student t。对估计两个平行轮廓之间的常数差的情况进行了扩展。
Abstract A Bayes solution is supplied for an estimation problem involving a sample from a multivariate normal population having an arbitrary unknown covariance matrix, but a vector mean whose components are all equal. Assuming that a particular unnormed prior density is a convenient expression for displaying prior ignorance, it is then demonstrated that a posterior interval for this common mean can be based on Student's t distribution. If prior information can be conveniently represented by a natural conjugate prior density, the posterior interval will also depend on Student's t. An extension is made to the case of estimating the constant difference between two parallel profiles.