Andrew Yiu: Semiparametric posterior corrections

Speaker: Andrew Yiu (University of Oxford)
Title: Semiparametric posterior corrections
Abstract: Semiparametric inference refers to the use of infinite-dimensional models to estimate finite-dimensional statistical functionals, which has gained particular popularity for handling causal problems. In empirical studies, nonparametric Bayesian methods such as BART (Bayesian additive regression trees) have performed strongly for point estimation, but the results for uncertainty quantification are mixed. The pivotal issue is the inherent “plug-in” nature of Bayesian inference, which means that the regularization employed in estimating high-dimensional nuisance parameters can induce a bias that bleeds into the estimation of the target functional. We introduce a method that post-processes an initial Bayesian posterior to correct the uncertainty quantification. The motivation is to fully leverage the adaptivity and predictive performance of nonparametric Bayes to tackle semiparametric problems with provision of asymptotic frequentist guarantees. Our approach could be interpreted as a stochastic version of semiparametric one-step estimation - we add a correction term to each posterior sample that incorporates both the efficient influence function and the Bayesian bootstrap. We illustrate the empirical performance of our method with the ACIC 2016 data analysis competition.