  Bayesian Generative AI (BayesGen-AI) methods are developed and applied to
Bayesian computation. BayesGen-AI reconstructs the posterior distribution by
directly modeling the parameter of interest as a mapping (a.k.a. deep learner)
from a large simulated dataset. This provides a generator that we can evaluate
at the observed data and provide draws from the posterior distribution. This
method applies to all forms of Bayesian inference including parametric models,
likelihood-free models, prediction and maximum expected utility problems.
Bayesian computation is then equivalent to high dimensional non-parametric
regression. Bayes Gen-AI main advantage is that it is density-free and
therefore provides an alternative to Markov Chain Monte Carlo. It has a number
of advantages over vanilla generative adversarial networks (GAN) and
approximate Bayesian computation (ABC) methods due to the fact that the
generator is simpler to learn than a GAN architecture and is more flexible than
kernel smoothing implicit in ABC methods. Design of the Network Architecture
requires careful selection of features (a.k.a. dimension reduction) and
nonlinear architecture for inference. As a generic architecture, we propose a
deep quantile neural network and a uniform base distribution at which to
evaluate the generator. To illustrate our methodology, we provide two real data
examples, the first in traffic flow prediction and the second in building a
surrogate for satellite drag data-set. Finally, we conclude with directions for
future research.
