UNIFORMLY MOST POWERFUL BAYESIAN TESTS.
UNIFORMLY MOST POWERFUL BAYESIAN TESTS.
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DOI：
10.1214/13-aos1123
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发表时间：
2013
影响因子：
4.5
通讯作者：
Johnson VE
中科院分区：
文献类型：
--
作者：
Johnson VE
一致最强大的检验是统计假设检验，在给定大小的所有检验中提供针对固定零假设的最大功效。在本文中，一致最大功效检验的概念通过将一致最大功效贝叶斯检验定义为最大化有利于备择假设的贝叶斯因子超过指定阈值的概率的检验而扩展到贝叶斯设置。像他们的经典对应，一致最强大的贝叶斯检验是最容易定义的单参数指数族模型，虽然扩展以外的这一类是可能的。一致最大功效检验和一致最大功效贝叶斯检验之间的联系可用于提供p值和贝叶斯因子之间的近似校准。最后，关于强依赖性的贝叶斯因子和p值样本大小的问题进行了讨论。
Uniformly most powerful tests are statistical hypothesis tests that provide the greatest power against a fixed null hypothesis among all tests of a given size. In this article, the notion of uniformly most powerful tests is extended to the Bayesian setting by defining uniformly most powerful Bayesian tests to be tests that maximize the probability that the Bayes factor, in favor of the alternative hypothesis, exceeds a specified threshold. Like their classical counterpart, uniformly most powerful Bayesian tests are most easily defined in one-parameter exponential family models, although extensions outside of this class are possible. The connection between uniformly most powerful tests and uniformly most powerful Bayesian tests can be used to provide an approximate calibration between p-values and Bayes factors. Finally, issues regarding the strong dependence of resulting Bayes factors and p-values on sample size are discussed.