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Revisiting Jeffreys’ Example: Bayes Test of the Normal Mean
The American Statistician ( IF 1.8 ) Pub Date : 2019-12-13 , DOI: 10.1080/00031305.2019.1687013
Malay Ghosh 1
Affiliation  

Abstract We revisit the classical problem of testing whether a normal mean is zero against all possible alternatives within a Bayesian framework. Jeffreys showed that the Bayes factor for this problem has a drawback with normal priors for the alternatives. He showed also that this deficiency is rectified when one uses a Cauchy prior instead. Noting that a Cauchy prior is an example of a scale-mixed normal prior, we want to examine whether or not scale-mixed normal priors can always overcome the deficiency of the Bayes factor. It turns out though that while mixing priors with polynomial tails can overcome this deficiency, those with exponential tails fail to do so. Examples are provided to illustrate this point.

中文翻译:

重温 Jeffreys 的例子:正态均值的贝叶斯检验

摘要 我们重新审视了在贝叶斯框架内针对所有可能的替代方案测试正常均值是否为零的经典问题。Jeffreys 表明,这个问题的贝叶斯因子在替代方案的正常先验中存在缺陷。他还表明,当人们使用柯西先验代替时,这一缺陷会得到纠正。注意到柯西先验是尺度混合正态先验的一个例子,我们想检查尺度混合正态先验是否总能克服贝叶斯因子的不足。事实证明,虽然将先验与多项式尾部混合可以克服这一缺陷,但那些具有指数尾部的却无法做到这一点。提供了一些例子来说明这一点。
更新日期:2019-12-13
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