Efficient acquisition rules for model-based approximate Bayesian computation

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 and running the simulation model 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 standard BO strategies are designed for optimisation and not specifically for ABC inference. Our paper addresses this gap in the literature. We propose to compute the uncertainty in the ABC posterior density, which is due to 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. Note: this work is currently under review in a journal and a full-length version is available as a nonrefereed pre-print (https://arxiv.org/abs/1704.00520)