  This paper discusses how two classes of approximate computation algorithms
can be adapted, in a modular fashion, to achieve exact statistical inference
from differentially private data products. Considered are approximate Bayesian
computation for Bayesian inference, and Monte Carlo Expectation-Maximization
for likelihood inference. Up to Monte Carlo error, inference from these
algorithms is exact with respect to the joint specification of both the
analyst's original data model, and the curator's differential privacy
mechanism. Highlighted is a duality between approximate computation on exact
data, and exact computation on approximate data, which can be leveraged by a
well-designed computational procedure for statistical inference.
