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. 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，提供了一种融入历史数据同时处理潜在先验-数据冲突的直观方法。然而，预先指定各分量的混合权重仍是一项关键挑战。理想情况下，混合权重应反映先验-数据冲突的程度，而这一程度往往事先未知，对混合先验的应用与接受构成了重大障碍。为应对这一挑战，我们提出了自适应混合（SAM）先验，该方法利用似然比检验统计量确定混合权重。SAM先验是数据驱动且自适应的：当先验-数据冲突证据不足（充分）时，倾向于选择信息性（非信息性）先验分量，从而实现动态信息借用。我们证明SAM先验在有限样本和大样本下均具有优良性质，并实现借用一致性。此外，SAM先验易于计算、数据驱动且无需校准，降低了数据挖掘风险。数值研究表明，SAM先验在有效处理先验-数据冲突方面优于现有方法。我们开发了免费提供的R语言包与网页应用程序，以促进SAM先验的使用。