The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power of $\alpha$, and then used as the prior distribution in the analysis of the replication data. Posterior distribution and Bayes factor hypothesis tests related to the power parameter $\alpha$ quantify the degree of compatibility between the original and replication study. Inferences for other parameters, such as effect sizes, dynamically borrow information from the original study. The degree of borrowing depends on the conflict between the two studies. The practical value of the approach is illustrated on data from three replication studies, and the connection to hierarchical modeling approaches explored. We generalize the known connection between normal power priors and normal hierarchical models for fixed parameters and show that normal power prior inferences with a beta prior on the power parameter $\alpha$ align with normal hierarchical model inferences using a generalized beta prior on the relative heterogeneity variance $I^2$. The connection illustrates that power prior modeling is unnatural from the perspective of hierarchical modeling since it corresponds to specifying priors on a relative rather than an absolute heterogeneity scale.

翻译：科学领域持续存在的复制危机增加了对复制研究方法论的关注。我们提出了一种基于功率先验的新型贝叶斯分析方法：将原始研究数据的似然函数进行$\alpha$次幂提升，并将其作为复制数据分析中的先验分布。与功率参数$\alpha$相关的后验分布及贝叶斯因子假设检验可量化原始研究与复制研究之间的一致性程度。对其他参数（如效应量）的推断能够动态地从原始研究中借用信息，借用程度取决于两项研究之间的冲突程度。本研究通过三个复制研究的数据展示了该方法的实际价值，并探讨了其与分层建模方法的关联。我们推广了已知的常态功率先验与固定参数常态分层模型之间的关联，并证明：当功率参数$\alpha$服从贝塔先验时，常态功率先验推断与使用广义贝塔先验处理相对异质性方差$I^2$的常态分层模型推断具有一致性。这一关联表明，从分层建模视角看，功率先验建模并不自然，因其对应于在相对而非绝对异质性尺度上设定先验分布。