Generative AI for Bayesian Computation

Generative AI (Gen-AI) methods are developed for Bayesian Computation. Gen-AI naturally applies to Bayesian models which can be easily simulated. First, we generate a large training dataset of data and parameters from the joint probability model. Secondly, we find a summary/sufficient statistic for dimensionality reduction. Thirdly, we use a deep neural network to uncover the inverse Bayes map between parameters and data. This finds the inverse posterior cumulative distribution function. Bayesian computation then is equivalent to high dimensional regression with dimensionality reduction (a.k.a feature selection) and nonlnearity (a.k.a. deep learning). The main advantage of Gen-AI is the ability to be density-free and hence avoids MCMC simulation of the posterior. Architecture design is important and we propose deep quantile NNs as a general framework for inference and decision making. To illustrate our methodology, we provide three examples: a stylized synthetic example, a traffic flow prediction problem and a satellite data-set. Finally, we conclude with directions for future research.