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制程度，目前尚未达成共识。我们提出了一种基于混合先验的、用于重复研究的新型贝叶斯方法。其核心思想是：将基于原始研究的后验分布与一个无信息分布混合，作为分析重复研究时的先验分布。混合权重则决定了原始数据与重复数据被合并的程度。本文提出了两种不同的策略：一种是固定混合权重；另一种则通过为混合权重本身分配先验分布来引入不确定性。此外，我们还展示了在此框架内如何利用贝叶斯因子对相关科学假设进行形式化检验，例如检验效应是否存在、混合权重是否为零（完全忽略原始数据）或为一（与原始数据完全合并）。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。我们的研究结果表明，混合先验是分析重复研究时其他贝叶斯方法（如分层模型和幂先验）的一种有价值且直观的替代方案。我们提供了免费开源的R软件包repmix，用于实现所提出的方法。