  Markov chain Monte Carlo (MCMC) is one of the main workhorses of
probabilistic inference, but it is notoriously hard to measure the quality of
approximate posterior samples. This challenge is particularly salient in black
box inference methods, which can hide details and obscure inference failures.
In this work, we extend the recently introduced bidirectional Monte Carlo
technique to evaluate MCMC-based posterior inference algorithms. By running
annealed importance sampling (AIS) chains both from prior to posterior and vice
versa on simulated data, we upper bound in expectation the symmetrized KL
divergence between the true posterior distribution and the distribution of
approximate samples. We present Bounding Divergences with REverse Annealing
(BREAD), a protocol for validating the relevance of simulated data experiments
to real datasets, and integrate it into two probabilistic programming
languages: WebPPL and Stan. As an example of how BREAD can be used to guide the
design of inference algorithms, we apply it to study the effectiveness of
different model representations in both WebPPL and Stan.
