论文标题
皮尔森贝叶斯因素：一种用于计算最小汇总统计数据的证据价值的分析公式
The Pearson Bayes factor: An analytic formula for computing evidential value from minimal summary statistics
论文作者
论文摘要
在贝叶斯假设检验中，统计模型的证据通过贝叶斯因子进行了量化，贝叶斯因子代表了与另一个竞争模型相比，该模型下观察到的数据的相对可能性。通常，计算贝叶斯因素很困难，因为在给定模型下计算数据的边际可能性需要在模型参数的先前分布上集成。在本文中，我利用了特定的先前分布选择，该选择允许贝叶斯因子在没有整体表示的情况下表达出来，并且我开发了一个简单的公式（Pearson Bayes因子），该公式仅需要在科学论文中通常报告的最小摘要统计数据，例如$ t $或$ f $评分和自由度。除了提出这一新结果外，我还提供了几个使用情况的示例，并报告了验证其性能的模拟研究。重要的是，皮尔森贝叶斯因子使应用研究人员能够从最小摘要数据中计算精确的贝叶斯因子，因此即使没有原始数据不可用，也可以轻松评估提供这些摘要统计数据的任何数据的证据价值。
In Bayesian hypothesis testing, evidence for a statistical model is quantified by the Bayes factor, which represents the relative likelihood of observed data under that model compared to another competing model. In general, computing Bayes factors is difficult, as computing the marginal likelihood of data under a given model requires integrating over a prior distribution of model parameters. In this paper, I capitalize on a particular choice of prior distribution that allows the Bayes factor to be expressed without integral representation and I develop a simple formula -- the Pearson Bayes factor -- that requires only minimal summary statistics commonly reported in scientific papers, such as the $t$ or $F$ score and the degrees of freedom. In addition to presenting this new result, I provide several examples of its use and report a simulation study validating its performance. Importantly, the Pearson Bayes factor gives applied researchers the ability to compute exact Bayes factors from minimal summary data, and thus easily assess the evidential value of any data for which these summary statistics are provided, even when the original data is not available.
