P Values for Composite Null Models
P Values for Composite Null Models
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DOI：
10.1080/01621459.2000.10474309
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发表时间：
2000-12
影响因子：
3.7
通讯作者：
M. J. Bayarri;J. Berger
中科院分区：
文献类型：
--
作者：
M. J. Bayarri;J. Berger
摘要研究了在假设模型参数未知的情况下，假设模型与数据的兼容性问题。最常用的兼容性度量是基于统计数据T的p值，其中较大的值被认为表明数据和模型不兼容。当null模型具有未知参数时，p值不是唯一定义的。在这种情况下计算p值的建议包括在频域侧使用插件p值和相似p值，在贝叶斯侧使用预测p值和后验预测p值。我们提出了条件预测p值和部分后验预测p值两种替代方法，并从贝叶斯和频率论的角度指出了它们的优点。
Abstract The problem of investigating compatibility of an assumed model with the data is investigated in the situation when the assumed model has unknown parameters. The most frequently used measures of compatibility are p values, based on statistics T for which large values are deemed to indicate incompatibility of the data and the model. When the null model has unknown parameters, p values are not uniquely defined. The proposals for computing a p value in such a situation include the plug-in and similar p values on the frequentist side, and the predictive and posterior predictive p values on the Bayesian side. We propose two alternatives, the conditional predictive p value and the partial posterior predictive p value, and indicate their advantages from both Bayesian and frequentist perspectives.