Generative AI for Bayesian Computation

Generative Bayesian Computation (GBC) provides a simulation-based approach to Bayesian inference. A Quantile Neural Network (QNN) is trained to map samples from a base distribution to the posterior distribution. Our method applies equally to parametric and likelihood-free models. By generating a large training dataset of parameter-output pairs inference is recast as a supervised learning problem of non-parametric regression. Generative quantile methods have a number of advantages over traditional approaches such as approximate Bayesian computation (ABC) or GANs. Primarily, quantile architectures are density-free and exploit feature selection using dimensionality reducing summary statistics. To illustrate our methodology, we analyze the classic normal-normal learning model and apply it to two real data problems, modeling traffic speed and building a surrogate model for a satellite drag dataset. We compare our methodology to state-of-the-art approaches. Finally, we conclude with directions for future research.