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 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 scientific hypotheses, such as tests regarding the presence or absence of an effect. 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靠性至关重要。然而，关于如何量化重复研究对原始结果的复现程度，目前尚未形成共识。本文提出了一种基于混合先验的新型贝叶斯方法。其核心思想是：在分析重复研究时，采用基于原始研究的后验分布与一个无信息分布的混合作为先验分布。混合权重则决定了原始数据与重复数据被合并的程度。我们提出了两种不同的策略：一种是固定混合权重；另一种则通过对混合权重本身赋予先验分布来引入不确定性。此外，本文还展示了如何在此框架内使用贝叶斯因子对科学假设（例如效应存在与否的检验）进行形式化检验。为展示该方法在实际中的应用，我们分析了三项重复研究的数据。研究结果表明，对于分析重复研究的其他贝叶斯方法（如分层模型和幂先验）而言，混合先验是一种有价值且直观的替代方案。我们提供了免费开源的R软件包repmix，用于实现所提出的方法。