  We present a new approach to semiparametric inference using corrected
posterior distributions. The method allows us to leverage the adaptivity,
regularization and predictive power of nonparametric Bayesian procedures to
estimate low-dimensional functionals of interest without being restricted by
the holistic Bayesian formalism. Starting from a conventional nonparametric
posterior, we target the functional of interest by transforming the entire
distribution with a Bayesian bootstrap correction. We provide conditions for
the resulting $\textit{one-step posterior}$ to possess calibrated frequentist
properties and specialize the results for several canonical examples: the
integrated squared density, the mean of a missing-at-random outcome, and the
average causal treatment effect on the treated. The procedure is
computationally attractive, requiring only a simple, efficient post-processing
step that can be attached onto any arbitrary posterior sampling algorithm.
Using the ACIC 2016 causal data analysis competition, we illustrate that our
approach can outperform the existing state-of-the-art through the propagation
of Bayesian uncertainty.
