Generalized Power Priors for Improved Bayesian Inference with Historical Data

Masanari Kimura; Howard Bondell

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arXiv · 2505.16244

Generalized Power Priors for Improved Bayesian Inference with Historical Data

Masanari Kimura·Howard Bondell

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Abstract

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 $\alpha$-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 $\alpha$ 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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BibTeX RIS

Masanari Kimura, Howard Bondell. 2025-05-22. Generalized Power Priors for Improved Bayesian Inference with Historical Data. https://arxiv.org/abs/2505.16244

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