Mixture priors provide an intuitive way to incorporate historical data while accounting for potential prior-data conflict by combining an informative prior with a non-informative prior. However, pre-specifying the mixing weight for each component remains a crucial challenge. Ideally, the mixing weight should reflect the degree of prior-data conflict, which is often unknown beforehand, posing a significant obstacle to the application and acceptance of mixture priors. To address this challenge, we introduce self-adapting mixture (SAM) priors that determine the mixing weight using likelihood ratio test statistics or Bayes factor. SAM priors are data-driven and self-adapting, favoring the informative (non-informative) prior component when there is little (substantial) evidence of prior-data conflict. Consequently, SAM priors achieve dynamic information borrowing. We demonstrate that SAM priors exhibit desirable properties in both finite and large samples and achieve information-borrowing consistency. Moreover, SAM priors are easy to compute, data-driven, and calibration-free, mitigating the risk of data dredging. Numerical studies show that SAM priors outperform existing methods in adopting prior-data conflicts effectively. We developed an R package and web application that are freely available to facilitate the use of SAM priors.

翻译：混合先验通过将信息性先验与非信息性先验相结合，在考虑潜在先验-数据冲突的同时，提供了一种整合历史数据的直观方法。然而，为每个分量预先指定混合权重仍是一个关键挑战。理想情况下，混合权重应反映先验-数据冲突的程度，但这一程度通常事先未知，这给混合先验的应用和接受带来了重大障碍。为应对这一挑战，我们引入了自适应混合（SAM）先验，它利用似然比检验统计量或贝叶斯因子来确定混合权重。SAM先验是数据驱动且自适应的：当先验-数据冲突的证据较少（或充分）时，它倾向于信息性（或非信息性）先验分量。因此，SAM先验实现了动态信息借用。我们证明了SAM先验在有限样本和大样本中均具有理想性质，并达到了信息借用一致性。此外，SAM先验易于计算、数据驱动且无需校准，降低了数据挖掘的风险。数值研究表明，SAM先验在有效应对先验-数据冲突方面优于现有方法。我们开发了免费可用的R包和网络应用程序，以方便SAM先验的使用。