AI-Powered Bayesian Inference

This document introduces a novel Bayesian statistical inference method that leverages Generative Artificial Intelligence (GAI) predictions. Instead of relying solely on limited observed data or traditional statistical models, the authors propose using GAI to create synthetic data, which then informs a non-parametric prior distribution within a Bayesian framework. This approach, termed AI-Powered Bayesian Inference, allows for robust uncertainty quantification and improved predictive inference by integrating the insights derived from AI-generated data. The research demonstrates the method's effectiveness through applications in medical diagnosis and astrophysics, showcasing its potential to enhance the predictive capabilities and inferential certainty of statistical analyses.