  In certain applications involving the solution of a Bayesian inverse problem,
it may not be possible or desirable to evaluate the full posterior, e.g. due to
the high computational cost of doing so. This problem motivates the use of
approximate posteriors that arise from approximating the data misfit or forward
model. We review some error bounds for random and deterministic approximate
posteriors that arise when the approximate data misfits and approximate forward
models are random.
