Generative AI for Bayesian Computation

We develop Generative AI (Gen-AI) methods for Bayesian Computation. Gen-AI naturally applies to Bayesian models which are easily simulated. We generate a large training dataset and together with deep neural networks we uncover the inverse Bayes map for inference and prediction. To do this, we require high dimensional regression methods and dimensionality reduction (a.k.a feature selection). The main advantage of Generative AI is its ability to be model-free and the fact that it doesn't rely on densities. Bayesian computation is replaced by pattern recognition of an input-output map. This map is learned from empirical model simulation. We show that Deep Quantile NNs provide a general framework for inference decision making. To illustrate our methodology, we provide three examples: a stylized synthetic example, a traffic flow prediction problem and we analyze the well-known Ebola data-set. Finally, we conclude with directions for future research.