随机贝叶斯因子：缘由、时机与方法
Stochastic Bayes factors: why, when, and how
- University of Trieste（的里雅斯特大学）
- Athens University of Economics and Business（雅典经济与商业大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文针对经典贝叶斯因子的应用局限，提出随机贝叶斯因子框架，通过理论推导与算法实现，经模拟及实际应用验证其较经典贝叶斯因子具备更优稳健性与预测可靠性。
AI中文摘要：
贝叶斯因子（Bayes factor, BF）是贝叶斯假设检验与模型选择的核心工具，但其实际应用常面临诸多挑战：经典BF高度依赖先验设定，无法与非正则先验结合使用，且通常通过任意证据尺度进行解释；此外，经典BF无法捕捉数据固有的不确定性，与频率学派p值类似，且主要反映先验预测表现而非后验预测表现。本文提出随机贝叶斯因子（stochastic Bayes factor, SBF），这一全新框架通过显式纳入重复数据的不确定性扩展了BF。形式上，SBF被定义为将BF从观测数据空间转换至重复数据空间的推前测度。该方法推广了先前的校准方案，同时强调后验预测重复作为一种稳健替代方案。本文建立了SBF的关键理论性质，包括模型一致性、兼容性与支配性，确保SBF保留理想的贝叶斯保证。随后提出了将SBF付诸实践的算法流程，以原则性方式指导模型区分，同时自然提供模型校准。模拟研究与实际应用均证实，与经典BF相比，SBF通过提供有价值的模型比较工具，具备更优的稳健性与预测可靠性。
英文摘要：
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.
