# Generalized Power Priors for Improved Bayesian Inference with Historical Data

arXiv: https://arxiv.org/abs/2505.16244 · HTML: https://mlsanity.com/paper/2505.16244/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 22 May 2025.

## Abstract (arXiv)

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.