# Supercharging Bayesian Inference with Reliable AI-Informed Priors

arXiv: https://arxiv.org/abs/2605.09834 · HTML: https://mlsanity.com/paper/2605.09834/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 32 references that are in the map.
- First posted on arXiv 11 May 2026.

## Builds on (most cited first, 16 of 16)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Retiring Adult: New Datasets for Fair Machine Learning](https://mlsanity.com/paper/2108.04884/) (2021)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Can Large Language Models Transform Computational Social Science?](https://mlsanity.com/paper/2305.03514/) (2023)
- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Can Unconfident LLM Annotations Be Used for Confident Conclusions?](https://mlsanity.com/paper/2408.15204/) (2024)
- [Using Imperfect Surrogates for Downstream Inference: Design-based Supervised Learning for Social Science Applications of Large Language Models](https://mlsanity.com/paper/2306.04746/) (2023)
- [General Bayesian Updating and the Loss-Likelihood Bootstrap](https://mlsanity.com/paper/1709.07616/) (2017)
- [Calibrating general posterior credible regions](https://mlsanity.com/paper/1509.00922/) (2015)
- [Scalable Nonparametric Sampling from Multimodal Posteriors with the Posterior Bootstrap](https://mlsanity.com/paper/1902.03175/) (2019)
- [AI-Powered Bayesian Inference](https://mlsanity.com/paper/2502.19231/) (2025)
- [Catalytic Priors: Using Synthetic Data to Specify Prior Distributions in Bayesian Analysis](https://mlsanity.com/paper/2208.14123/) (2022)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [How many patients could we save with LLM priors?](https://mlsanity.com/paper/2509.04250/) (2025)
- [Synthetic Data, Information, and Prior Knowledge: Why Synthetic Data Augmentation to Boost Sample Doesn't Work for Statistical Inference](https://mlsanity.com/paper/2603.18345/) (2026)

## Built on by (most cited first, 1 of 1)

- [Empirical Likelihood with Generative AI](https://mlsanity.com/paper/2606.00425/) (2026)

## Abstract (arXiv)

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.