  Parameter inference, i.e. inferring the posterior distribution of the
parameters of a statistical model given some data, is a central problem to many
scientific disciplines. Generative models can be used as an alternative to
Markov Chain Monte Carlo methods for conducting posterior inference, both in
likelihood-based and simulation-based problems. However, assessing the accuracy
of posteriors encoded in generative models is not straightforward. In this
paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage
testing as a method to estimate coverage probabilities of generative posterior
estimators. Our method differs from previously-existing coverage-based methods,
which require posterior evaluations. We prove that our approach is necessary
and sufficient to show that a posterior estimator is accurate. We demonstrate
the method on a variety of synthetic examples, and show that TARP can be used
to test the results of posterior inference analyses in high-dimensional spaces.
We also show that our method can detect inaccurate inferences in cases where
existing methods fail.
