改进历史数据融合的贝叶斯推断方法，提升模型适应性。
Generalized Power Priors for Improved Bayesian Inference with Historical Data
- 用α-散度替代KL散度，更灵活地融合历史数据。
- 理论证明后验分布是测地线路径上的最优解。
- 适合需要动态调整历史数据权重的研究场景。
幂先验是一类用于在贝叶斯框架中融合历史数据与当前数据的信息先验，其通过一个幂参数控制历史数据的影响，具备灵活性和可适应性。幂先验的一个关键性质是，其后验分布最小化了两个伪后验分布之间的线性组合的KL散度：一个忽略历史数据，另一个完全纳入历史数据。本文将该框架扩展为将后验分布视为Amari α-散度（KL散度的推广）线性组合的最小化器。我们证明这一推广可带来性能提升，允许数据自适应选择合适的α参数。本文建立了广义幂后验的理论性质，包括其作为概率分布黎曼流形上广义测地线的行为，为该方法提供了新的几何解释。
原文摘要 · Abstract (English)
The power prior is a class of informative priors designed to incorporate historical data alongside current data in a Bayesian framework. It includes a power parameter that controls the influence of historical data, providing flexibility and adaptability. A key property of the power prior is that the resulting posterior minimizes a linear combination of KL divergences between two pseudo-posterior distributions: one ignoring historical data and the other fully incorporating it. We extend this framework by identifying the posterior distribution as the minimizer of a linear combination of Amari's $α$-divergence, a generalization of KL divergence. We show that this generalization can lead to improved performance by allowing for the data to adapt to appropriate choices of the $α$ parameter. Theoretical properties of this generalized power posterior are established, including behavior as a generalized geodesic on the Riemannian manifold of probability distributions, offering novel insights into its geometric interpretation.
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