A1613
Title: Generative quantile Bayes
Authors: Jungeum Kim - NCSU (United States) [presenting]
Percy Zhai - The University of Chicago (United States)
Veronika Rockova - University of Chicago (United States)
Abstract: A multivariate posterior sampling procedure is developed through deep generative quantile learning. Simulation proceeds implicitly through a push-forward mapping that can transform i.i.d. random vector samples from the posterior. Monge-Kantorovich depth in multivariate quantiles is utilized to directly sample from Bayesian credible sets, a unique feature not offered by typical posterior sampling methods. To enhance the training of the quantile mapping, a neural network is designed that automatically performs summary statistic extraction. This additional neural network structure provides performance benefits, including support shrinkage (contraction of the posterior approximation) as the observation sample size increases. The usefulness of the approach is demonstrated on several examples where the absence of likelihood renders classical MCMC infeasible. Frequentist theoretical justifications are provided for the quantile learning framework, including consistency of the estimated vector quantile, of the recovered posterior distribution, and of the corresponding Bayesian credible sets.
