🤖 AI Summary
本文提出随机贝叶斯因子(SBF)解决传统贝叶斯因子依赖先验、无法处理不适当先验及忽视数据不确定性等问题，通过复制数据引入不确定性，提高模型比较的稳健性和预测可靠性。
📝 Abstract
The Bayes factor (BF) is a central tool in Bayesian hypothesis testing and model selection, yet its practical use is often challenged. Classical BFs depend heavily on prior specification, cannot be applied with improper priors, and are typically interpreted through arbitrary evidence scales. Moreover, they fail to capture uncertainty inherent in the data, leading to an analogy with frequentist p-values, and primarily reflect prior-predictive rather than posterior-predictive performance. We introduce the stochastic Bayes factor (SBF), a new framework that extends the BF by explicitly incorporating uncertainty via replicated data. Formally, the SBF is defined as a push-forward measure transferring the BF from the observed data space to that of replications. This approach generalizes previous calibration proposals, while emphasizing posterior-predictive replication as a robust alternative. We establish key theoretical properties, including model consistency, compatibility and dominance, ensuring that SBFs preserve desirable Bayesian guarantees. An algorithmic routine is then proposed to operationalize the SBF, guiding model discrimination in a principled way while naturally providing model calibration. Simulation studies and real applications confirm that the SBF offers improved robustness and predictive reliability compared to the classical BF, by providing a valuable tool for model comparison.