Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables
Frequentist performance of Bayesian confidence intervals for comparing proportions in 2 x 2 contingency tables
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DOI：
10.1111/j.1541-0420.2005.031228.x
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发表时间：
2005-06-01
期刊：
影响因子：
1.9
通讯作者：
Min, YY
中科院分区：
文献类型：
--
作者：
Agresti, A;Min, YY
本文从频率论的角度研究了2 × 2列联表中比例、相对风险和比值比差异的贝叶斯置信区间（ci）的性能。我们考虑了两个二项参数的beta先验、对数正态先验和相关先验。我们的目标是分析在不考虑真实关联参数值的情况下，先前参数的某些设置是否倾向于提供良好的覆盖性能。对于相对风险和优势比，出于不变性的原因，我们推荐尾部间隔高于最高后验密度（HPD）间隔。当影响很大时，为了防止潜在的非常低的覆盖概率，最好使用扩散先验，我们建议使用Jeffreys先验。否则，对于相对较小的样本，使用更多信息（甚至均匀）先验的贝叶斯ci往往比基于反转分数测试的频率主义者ci表现更差，后者在这些参数上表现一致。
This article investigates the performance, in a frequentist sense, of Bayesian confidence intervals (CIs) for the difference of proportions, relative risk, and odds ratio in 2 x 2 contingency tables. We consider beta priors, logit-normal priors, and related correlated priors for the two binomial parameters. The goal was to analyze whether certain settings for prior parameters tend to provide good coverage performance regardless of the true association parameter values. For the relative risk and odds ratio, we recommend tail intervals over highest posterior density (HPD) intervals, for invariance reasons. To protect against potentially very poor coverage probabilities when the effect is large, it is best to use a diffuse prior, and we recommend the Jeffreys prior. Otherwise, with relatively small samples, Bayesian CIs using more informative (even uniform) priors tend to have poorer performance than the frequentist CIs based on inverting score tests, which perform uniformly quite well for these parameters.