Replication of scientific studies is important for assessing the credibility of their results. However, there is no consensus on how to quantify the extent to which a replication study replicates an original result. We propose a novel Bayesian approach for replication studies based on mixture priors. The idea is to use a mixture of the posterior distribution based on the original study and a non-informative distribution as the prior for the analysis of the replication study. The mixture weight then determines the extent to which the original and replication data are pooled. Two distinct strategies are presented: one with fixed mixture weights, and one that introduces uncertainty by assigning a prior distribution to the mixture weight itself. Furthermore, it is shown how within this framework Bayes factors can be used for formal testing of relevant scientific hypotheses, such as tests on the presence or absence of an effect or whether the mixture weight equals zero (completely discounting the original data) or one (fully pooling with the original data). To showcase the practical application of the methodology, we analyze data from three replication studies. Our findings suggest that mixture priors are a valuable and intuitive alternative to other Bayesian methods for analyzing replication studies, such as hierarchical models and power priors. We provide the free and open source R package repmix that implements the proposed methodology.

翻译：科学研究的可重复性对于评估其结果的可信度至关重要。然而，目前尚无共识来量化复制研究在多大程度上复现了原始结果。我们提出了一种基于混合先验的贝叶斯新方法用于复制研究。其核心思想是利用原始研究后验分布与非信息性分布的混合作为复制研究分析的先验分布，其中混合权重决定了原始数据与复制数据在何种程度上被合并。我们提出了两种不同的策略：一种是固定混合权重，另一种是通过为混合权重本身设定先验分布来引入不确定性。此外，我们展示了在此框架下如何利用贝叶斯因子对相关科学假设进行正式检验，例如检验效应的存在与否，或混合权重是否为零（完全忽略原始数据）或为一（完全合并原始数据）。为展示该方法的应用实践，我们分析了来自三项复制研究的数据。研究结果表明，混合先验是分析复制研究的其他贝叶斯方法（如层次模型和幂先验）的一种有价值且直观的替代方案。我们提供了实现该方法的开源R包repmix。