The Bayesian two-sample t test
The Bayesian two-sample t test
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DOI：
10.1198/000313005x55233
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发表时间：
2005-08-01
影响因子：
1.8
通讯作者：
Westfall, PH
中科院分区：
文献类型：
--
作者：
Gönen, M;Johnson, WO;Westfall, PH
本文介绍了双侧点零检验问题的贝叶斯公式是如何产生合方差两样本t统计量的，并着重于教学。我们确定了一个合理和有用的先验，给出了一个闭合形式的贝叶斯因子，该因子可以分别在零假设和替代假设下写成两样本t统计量的分布。这为双样本t统计量提供了贝叶斯动机，到目前为止，该统计量一直被掩盖为更复杂的线性模型的特例，或者仅粗略地通过解析或蒙特卡罗近似给出。由此得到的贝叶斯检验公式很容易在实践中应用，也很容易在强调贝叶斯方法的入门课程中教授。先验概率易于使用且易于推导，并且后验概率很容易使用现有的软件计算，在某些情况下使用电子表格。
This article shows how the pooled-variance two-sample t statistic arises from a Bayesian formulation of the two-sided point null testing problem, with emphasis on teaching. We identify a reasonable and useful prior giving a closed-form Bayes factor that can be written in terms of the distribution of the two-sample t statistic under the null and alternative hypotheses, respectively. This provides a Bayesian motivation for the two-sample t statistic, which has heretofore been buried as a special case of more complex linear models, or given only roughly via analytic or Monte Carlo approximations. The resulting formulation of the Bayesian test is easy to apply in practice, and also easy to teach in an introductory course that emphasizes Bayesian methods. The priors are easy to use and simple to elicit, and the posterior probabilities are easily computed using available software, in some cases using spreadsheets.