  It is important to estimate the errors of probabilistic inference algorithms.
Existing diagnostics for Markov chain Monte Carlo methods assume inference is
asymptotically exact, and are not appropriate for approximate methods like
variational inference or Laplace's method. This paper introduces a diagnostic
based on repeatedly simulating datasets from the prior and performing inference
on each. The central observation is that it is possible to estimate a symmetric
KL-divergence defined over these simulations.
