Posterior convergence given the mean
Posterior convergence given the mean
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给定均值的后验收敛
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
J. Ghosh
中科院分区：
文献类型：
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作者：
B. Clarke;J. Ghosh
对于各种应用，人们希望知道ω的渐近行为
（θX -），参数θ的后验密度，给定数据的平均值X -，而不是整个数据集。这里我们证明ω
（θ| X -|）在L1意义下是渐近正态的，我们确定了极限正态的均值及其渐近方差。主要结果首先在假设X1，…，X n，.是独立的和相同的;适当的修改，以获得不同的情况下的结果分别给出。我们的研究结果可用于构造近似HPD（最高后验密度）集的参数，这是使用在统计理论的标准化教育考试。它们还可用于显示在平均值渐进非正的条件下两个测试项之间的协方差。这对构建项目独立性测试有影响。
For various applications one wants to know the asymptotic behavior of ω
(θX - ), the posterior density of a parameter θ given the mean X - of the data rather than the full data set. Here we show that ω
(θ|X - |) is asymptotically normal in an L 1 sense, and we identify the mean of the limiting normal and its asymptotic variance. The main results are first proved assuming that X 1 ,...,X n ,... are independent and identical; suitable modifications to obtain results for the nonidentical case are given separately. Our results may be used to construct approximate HPD (highest posterior density) sets for the parameter which is of use in the statistical theory of standardized educational tests. They may also be used to show the covariance between two test items conditioned on the mean is asymptotically nonpositive. This has implications for constructing tests of item independence.