Supercharging Bayesian Inference with Reliable AI-Informed Priors

Authors: Jongwoo Choi, Sean O'Hagan

arXiv · PDF

Summary

The authors tackle a problem that comes up when you want to use AI model predictions as prior beliefs for Bayesian inference: the AI might be wrong, and that error gets baked into your statistical conclusions. They propose "rectifying" the AI-generated distribution before using it as a prior—essentially correcting for known biases in the model's outputs. They show that this rectified prior reduces bias in the resulting posterior estimates, improves the coverage of credible intervals (the intervals actually contain the true value as often as they should), and boosts predictive performance on a real medical classification task.

Main takeaways:

• Standard practice of using AI predictions directly as priors can propagate model errors into your statistical inference
• The rectification step corrects the AI's output distribution before building a prior, reducing downstream bias
• They prove Gaussian asymptotics for the posterior and derive expressions for centering bias under their framework
• Empirical results show better credible interval coverage and improved predictive performance on skin disease classification
• The method works with flexible prior structures like Dirichlet processes

Relevance

Not directly related to my persona or midtraining work—this is about combining AI predictions with classical statistical inference rather than installing or steering behavior in language models.

Abstract

arXiv:2605.09834v1 Announce Type: new Abstract: Modern predictive systems encode beliefs that can act as useful prior information for statistical inference in data-limited settings. Using them for prior construction introduces a tradeoff: an informative prior built from a predictive model can sharpen inference from limited data, but also risks propagating error from the model into the posterior. We propose a framework for AI-informed prior elicitation that mitigates this tension by rectifying the AI-induced law that generates synthetic data before using it to inform a prior. The rectified law can be embedded into synthetic data-driven prior elicitation techniques, including as a base measure in a Dirichlet process (DP) prior on the data-generating process. We refer to the resulting prior and corresponding posterior as the rectified AI prior and rectified AI posterior. We establish Gaussian asymptotics for the rectified AI posterior under non-vanishing prior strength and derive a first-order expression for its centering bias. Our rectified AI priors substantially reduce bias compared to standard approaches, improve the coverage of credible intervals, and make AI-powered prior information more reliable. We additionally apply the rectified AI prior to a real skin disease classification task and show that it can meaningfully boost predictive performance.