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.

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