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：科学领域的持续复制危机推动了对复制研究方法论的兴趣。我们提出一种基于幂先验的新型贝叶斯分析方法：将原始研究数据的似然函数提升至 $\alpha$ 次幂，并将其作为复制数据分析中的先验分布。与幂参数 $\alpha$ 相关的后验分布和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。对效应量等其他参数的推断，将动态借用原始研究的信息。借用程度取决于两项研究之间的冲突。通过三项复制研究的数据验证了该方法的实用价值，并探讨了其与层次建模方法的关联。我们推广了固定参数下正态幂先验与正态层次模型之间的已知联系，并证明：在幂参数 $\alpha$ 服从贝塔先验的条件下，正态幂先验推断与使用广义贝塔先验作用于相对异质性方差 $I^2$ 的正态层次模型推断结果一致。该联系揭示了幂先验建模在层次建模视角下的非自然性——因其对应的是在相对异质性尺度（而非绝对异质性尺度）上指定先验分布。