从频率主义p值中提取贝叶斯证据
Extracting Bayesian Evidence from Frequentist p-Values
AI总结：
研究从频率主义p值中提取贝叶斯证据的方法，核心是杰弗里斯近似贝叶斯因子（JAB），它在单位信息先验下仅需p值和有效样本量，经大量测试表明能很好近似客观贝叶斯因子，为p值提供样本量敏感补充且在选择性停止时也有效。
AI中文摘要：
p值和贝叶斯因子是衡量证据的指标，通常被认为在哲学和数学上不兼容。我们重新审视杰弗里斯近似贝叶斯因子（JAB），它可连接这两种客观假设检验范式。在单位信息先验下，该近似仅需p值和有效样本量\(n_{eff}\)。我们阐明其应用的核心假设和边界条件，并通过大量测试表明JAB能很好地近似客观贝叶斯因子。p值与JAB的联系表明，p值所暗示的证据强烈依赖于\(n_{eff}\)。JAB为p值提供了一种廉价、对样本量敏感的补充，可从常规统计数据计算得出，即使在选择性停止情况下也有效。
英文摘要：
The $p$-value and the Bayes factor are measures of evidence that are often considered to be philosophically and mathematically incompatible: The $p$-value quantifies conflict between data and $H_0$ ("surprise"), whereas the Bayes factor quantifies the relative predictive accuracy of $H_0$ versus $H_1$ ("evidence"). We revisit Jeffreys's Approximate Bayes factor (JAB) -- a simple, largely overlooked approximation dating back to the 1930s -- which connects these two paradigms for objective hypothesis testing of the existence of an effect. Under a unit-information prior the approximation requires only the $p$-value and the effective sample size $n_\text{eff}$. We clarify the core assumptions and boundary conditions for the application of JAB and show across 704 published $t$-tests and 39 comparisons of proportions that JAB approximates objective Bayes factors remarkably well. The connection between $p$-values and JAB has a practical implication: The evidence implied by a $p$-value depends strongly on $n_\text{eff}$. Conventional verbal labels for $p$-values (e.g., "strong surprise" for .001 < $p$ < .01) correspond to similarly graded Bayes factors only around $n_\text{eff} \approx 8$; for larger samples the same $p$-value implies weaker evidence. In moderately sized to large samples, $p > .10$ can amount to moderate or even strong evidence for $H_0$. JAB offers a cheap, sample-size-sensitive supplement to $p$-values, computable from routinely reported statistics, that remains valid even under optional stopping.
