A prior for the variance in hierarchical models
A prior for the variance in hierarchical models
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DOI：
10.2307/3316112
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发表时间：
1999-09-01
影响因子：
0.6
通讯作者：
Daniels, MJ
中科院分区：
文献类型：
--
作者：
Daniels, MJ
在贝叶斯分层模型和方差分量模型中，方差的先验分布的选择是重要的，也是相当困难的。对于很少有先验信息的情况，通常选择“非信息”类型的先验。“非信息”先验已经被许多作者讨论过，并在许多情况下使用。然而，必须小心使用这些先验分布，因为许多先验分布是不正确的，因此可能导致不正确的后验分布。此外，在小样本中，这些先验可以是“信息”。在本文中，我们研究了一个适当的“模糊”先验，均匀收缩先验（Strawderman 1971; Christiansen & Morris 1997）。我们讨论了它的性质，并显示如何后验分布的共同层次模型使用此先验导致适当的后验分布。我们还说明了一个正常的层次模型，包括测试和估计的吸引力的频率属性。最后，我们将其推广到协方差矩阵的多变量情况之前。
The choice of prior distributions for the variances can be important and quite difficult in Bayesian hierarchical and variance component models. For situations where little prior information is available, a 'noninformative' type prior is usually chosen. 'Noninformative' priors have been discussed by many authors and used in many contexts. However, care must be taken using these prior distributions as many are improper and thus, can lead to improper posterior distributions. Additionally, in small samples, these priors can be 'informative'. In this paper, we investigate a proper 'vague' prior, the uniform shrinkage prior (Strawderman 1971; Christiansen & Morris 1997). We discuss its properties and show how posterior distributions for common hierarchical models using this prior lead to proper posterior distributions. We also illustrate the attractive frequentist properties of this prior for a normal hierarchical model including testing and estimation. To conclude, we generalize this prior to the multivariate situation of a covariance matrix.