Assessing replication success via skeptical mixture priors

There is growing interest in the analysis of replication studies aimed at reassessing original findings across a wide range of scientific disciplines. In the context of hypothesis testing for effect sizes, two Bayesian approaches stand out for their principled use of the Bayes factor (BF): the replication BF and the skeptical BF. The latter, built around the skeptical prior, represents the perspective of an investigator who remains unconvinced by the original results and seeks to critically reassess them. In this paper, we adopt the skeptical viewpoint and introduce a novel mixture prior that incorporates skepticism while offering control over prior-data conflict. We study the consistency properties of the resulting skeptical mixture Bayes factor and examine its relationship to the standard skeptical BF. Through a focused simulation study, we conduct a sensitivity analysis of the skeptical mixture BF with respect to prior-data conflict, covering a range of plausible experimental scenarios. Our results show broad agreement with the standard skeptical BF under typical conditions. However, in situations where the standard skeptical BF suffers from severe prior-data conflict, our approach can yield a meaningful adjustment in the reported strength of replication success. Finally, we illustrate the practical application of our method using case studies from the Social Sciences Replication Project.