Title: Efficient acquisition rules for model-based approximate Bayesian computation,
Abstract: Approximate Bayesian computation (ABC) is a method for Bayesian inference
when the likelihood is unavailable but simulating from the model is possible.
However, many ABC algorithms require a large number of simulations, which can
be costly. To reduce the computational cost, Bayesian optimisation (BO) and
surrogate models such as Gaussian processes have been proposed. Bayesian
optimisation enables one to intelligently decide where to evaluate the model
next but common BO strategies are not designed for the goal of estimating the
posterior distribution. Our paper addresses this gap in the literature. We
propose to compute the uncertainty in the ABC posterior density, which is due
to a lack of simulations to estimate this quantity accurately, and define a
loss function that measures this uncertainty. We then propose to select the
next evaluation location to minimise the expected loss. Experiments show that
the proposed method often produces the most accurate approximations as compared
to common BO strategies.