  We present extensive empirical evidence showing that current Bayesian
simulation-based inference algorithms can produce computationally unfaithful
posterior approximations. Our results show that all benchmarked algorithms --
(Sequential) Neural Posterior Estimation, (Sequential) Neural Ratio Estimation,
Sequential Neural Likelihood and variants of Approximate Bayesian Computation
-- can yield overconfident posterior approximations, which makes them
unreliable for scientific use cases and falsificationist inquiry. Failing to
address this issue may reduce the range of applicability of simulation-based
inference. For this reason, we argue that research efforts should be made
towards theoretical and methodological developments of conservative approximate
inference algorithms and present research directions towards this objective. In
this regard, we show empirical evidence that ensembling posterior surrogates
provides more reliable approximations and mitigates the issue.
