  Scientists continue to develop increasingly complex mechanistic models to
reflect their knowledge more realistically. Statistical inference using these
models can be challenging since the corresponding likelihood function is often
intractable and model simulation may be computationally burdensome.
Fortunately, in many of these situations, it is possible to adopt a surrogate
model or approximate likelihood function. It may be convenient to conduct
Bayesian inference directly with the surrogate, but this can result in bias and
poor uncertainty quantification. In this paper we propose a new method for
adjusting approximate posterior samples to reduce bias and produce more
accurate uncertainty quantification. We do this by optimizing a transform of
the approximate posterior that maximizes a scoring rule. Our approach requires
only a (fixed) small number of complex model simulations and is numerically
stable. We demonstrate good performance of the new method on several examples
of increasing complexity.
