POSTERIOR PREDICTIVE P-VALUES
POSTERIOR PREDICTIVE P-VALUES
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DOI：
10.1214/aos/1176325622
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发表时间：
1994-09-01
影响因子：
4.5
通讯作者：
MENG, XL
中科院分区：
文献类型：
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作者：
MENG, XL
本文推广了Rubin的工作，探索了经典p值的贝叶斯对应，即零假设下检验统计量的尾区概率。贝叶斯公式使用数据的后验预测复制，允许“检验统计”依赖于数据和未知(干扰)参数，从而允许直接测量样本和总体数量之间的差异。然后，在重复数据和(干扰)参数的联合后验分布下，求出“检验统计量”的尾区概率，两者都是以零假设为条件的。这种后验预测p值也可以被视为经典p值的后验均值，在零假设下对(讨厌)参数的后验分布进行平均，因此它提供了一种处理讨厌参数的一般方法。用两个经典例子，包括Behrens-Fisher问题，说明了后验预测p值及其一些有趣的性质，这也揭示了一些经典p值的一种新的(贝叶斯)解释。文中还给出了它在多重归因推理中的应用。频率评估表明，一般来说，如果复制是由新的(讨厌的)参数和新数据定义的，则α水平后验预测检验的I型频率误差通常接近但小于α，并且永远不会超过2α。
Extending work of Rubin, this paper explores a Bayesian counterpart of the classical p-value, namely, a tail-area probability of a ''test statistic'' under a null hypothesis. The Bayesian formulation, using posterior predictive replications of the data, allows a ''test statistic'' to depend on both data and unknown (nuisance) parameters and thus permits a direct measure of the discrepancy between sample and population quantities. The tail-area probability for a ''test statistic'' is then found under the joint posterior distribution of replicate data and the (nuisance) parameters, both conditional on the null hypothesis. This posterior predictive p-value can also be viewed as the posterior mean of a classical p-value, averaging over the posterior distribution of(nuisance) parameters under the null hypothesis, and thus it provides one general method for dealing with nuisance parameters. Two classical examples, including the Behrens-Fisher problem, are used to illustrate the posterior predictive p-value and some of its interesting properties, which also reveal a new (Bayesian) interpretation for some classical p-values. An application to multiple-imputation inference is also presented. A frequency evaluation shows that, in general, if the replication is defined by new (nuisance) parameters and new data, then the Type I frequentist error of an alpha-level posterior predictive test is often close to but less than alpha and will never exceed 2 alpha.