# AI-Powered Bayesian Inference

arXiv: https://arxiv.org/abs/2502.19231 · HTML: https://mlsanity.com/paper/2502.19231/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 68 references that are in the map.
- First posted on arXiv 26 Feb 2025.

## Builds on (most cited first, 13 of 13)

- [Prediction-Powered Inference](https://mlsanity.com/paper/2301.09633/) (2023)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [PPI++: Efficient Prediction-Powered Inference](https://mlsanity.com/paper/2311.01453/) (2023)
- [Cross-Prediction-Powered Inference](https://mlsanity.com/paper/2309.16598/) (2023)
- [Martingale posterior distributions](https://mlsanity.com/paper/2103.15671/) (2021)
- [General Bayesian Updating and the Loss-Likelihood Bootstrap](https://mlsanity.com/paper/1709.07616/) (2017)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [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)
- [Bayesian Bootstrap Spike-and-Slab LASSO](https://mlsanity.com/paper/2011.14279/) (2020)
- [An MCMC Approach to Classical Estimation](https://mlsanity.com/paper/2301.07782/) (2023)
- [Adaptive Uncertainty Quantification for Generative AI](https://mlsanity.com/paper/2408.08990/) (2024)
- [Power-Expected-Posterior Priors for Generalized Linear Models](https://mlsanity.com/paper/1508.00793/) (2015)

## Built on by (most cited first, 8 of 8)

- [A Unified Framework for Inference with General Missingness Patterns and Machine Learning Imputation](https://mlsanity.com/paper/2508.15162/) (2025)
- [Do We Really Even Need Data? A Modern Look at Drawing Inference with Predicted Data](https://mlsanity.com/paper/2512.05456/) (2025)
- [Supercharging Bayesian Inference with Reliable AI-Informed Priors](https://mlsanity.com/paper/2605.09834/) (2026)
- [Foundation Priors](https://mlsanity.com/paper/2512.01107/) (2025)
- [Adaptive Querying with AI Persona Priors](https://mlsanity.com/paper/2605.00696/) (2026)
- [Empirical Likelihood with Generative AI](https://mlsanity.com/paper/2606.00425/) (2026)
- [Private Generative Bootstrap via Blocking](https://mlsanity.com/paper/2608.02480/) (2026)
- [Learning a Size-Weight Frontier for Synthetic-Augmented Inference](https://mlsanity.com/paper/2608.28576/) (2026)

## Abstract (arXiv)

The advent of Generative Artificial Intelligence (GAI) has heralded an inflection point that changed how society thinks about knowledge acquisition. While GAI cannot be fully trusted for decision-making, it may still provide valuable information that can be integrated into a decision pipeline. Rather than seeing the lack of certitude and inherent randomness of GAI as a problem, we view it as an opportunity. Indeed, variable answers to given prompts can be leveraged to construct a prior distribution which reflects assuredness of AI predictions. This prior distribution may be combined with tailored datasets for a fully Bayesian analysis with an AI-driven prior. In this paper, we explore such a possibility within a non-parametric Bayesian framework. The basic idea consists of assigning a Dirichlet process prior distribution on the data-generating distribution with AI generative model as its baseline. Hyper-parameters of the prior can be tuned out-of-sample to assess the informativeness of the AI prior. Posterior simulation is achieved by computing a suitably randomized functional on an augmented data that consists of observed (labeled) data as well as fake data whose labels have been imputed using AI. This strategy can be parallelized and rapidly produces iid samples from the posterior by optimization as opposed to sampling from conditionals. Our method enables (predictive) inference and uncertainty quantification leveraging AI predictions in a coherent probabilistic manner.