  Current literature on posterior approximation for Bayesian inference offers
many alternative methods. Does our chosen approximation scheme work well on the
observed data? The best existing generic diagnostic tools treating this kind of
question by looking at performance averaged over data space, or otherwise lack
diagnostic detail. However, if the approximation is bad for most data, but good
at the observed data, then we may discard a useful approximation. We give
graphical diagnostics for posterior approximation at the observed data. We
estimate a "distortion map" that acts on univariate marginals of the
approximate posterior to move them closer to the exact posterior, without
recourse to the exact posterior.
