Classical and Bayesian interpretation of the Birge test of consistency and its generalized version for correlated results from interlaboratory evaluations
Classical and Bayesian interpretation of the Birge test of consistency and its generalized version for correlated results from interlaboratory evaluations
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Birge 一致性检验的经典和贝叶斯解释及其实验室间评估相关结果的广义版本
DOI：
10.1088/0026-1394/45/3/001
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发表时间：
2008
期刊：
影响因子：
2.4
通讯作者：
K. Sommer
中科院分区：
文献类型：
--
作者：
R. Kacker;A. Forbes;R. Kessel;K. Sommer
著名的实验室间评估结果一致性测试是 Birge 测试，以其开发者物理学家 Raymond T Birge 的名字命名。我们表明，Birge 一致性检验可以解释为原假设（结果的方差小于或等于其规定值）与备择假设（结果的方差大于其规定值）的经典检验。假设检验的现代协议是计算检验统计量的经典 p 值。 p 值是在概念重复中实现检验统计量的值等于或大于检验统计量的实现（观察到）值的原假设下的最大概率。当 p 值太小时，原假设将被拒绝。有趣的是，我们发现，Birge 检验统计量的经典 p 值等于原假设的贝叶斯后验概率，该原假设基于为未知统计参数适当选择的非信息性不正确先验分布。因此，Birge 检验也可以解释为原假设的贝叶斯检验。 Birge 一致性检验是为那些结果不相关的实验室间评估而开发的。我们提出了相关和不相关结果一致性的一般测试。然后我们证明一般检验统计量的经典 p 值等于基于非信息性先验分布的原假设的贝叶斯后验概率。一般测试可以检查实验室间评估相关结果的一致性。 Birge 测试是一般测试的一个特例。
A well-known test of consistency in the results from an interlaboratory evaluation is the Birge test, named after its developer Raymond T Birge, a physicist. We show that the Birge test of consistency may be interpreted as a classical test of the null hypothesis that the variances of the results are less than or equal to their stated values against the alternative hypothesis that the variances of the results are greater than their stated values. A modern protocol for hypothesis testing is to calculate the classical p-value of the test statistic. The p-value is the maximum probability under the null hypothesis of realizing in conceptual replications a value of the test statistic equal to or larger than the realized (observed) value of the test statistic. The null hypothesis is rejected when the p-value is too small. We show that, interestingly, the classical p-value of the Birge test statistic is equal to the Bayesian posterior probability of the null hypothesis based on suitably chosen non-informative improper prior distributions for the unknown statistical parameters. Thus the Birge test may be interpreted also as a Bayesian test of the null hypothesis. The Birge test of consistency was developed for those interlaboratory evaluations where the results are uncorrelated. We present a general test of consistency for both correlated and uncorrelated results. Then we show that the classical p-value of the general test statistic is equal to the Bayesian posterior probability of the null hypothesis based on non-informative prior distributions. The general test makes it possible to check the consistency of correlated results from interlaboratory evaluations. The Birge test is a special case of the general test.