  Bayesian experimental design involves the optimal allocation of resources in
an experiment, with the aim of optimising cost and performance. For implicit
models, where the likelihood is intractable but sampling from the model is
possible, this task is particularly difficult and therefore largely unexplored.
This is mainly due to technical difficulties associated with approximating
posterior distributions and utility functions. We devise a novel experimental
design framework for implicit models that improves upon previous work in two
ways. First, we use the mutual information between parameters and data as the
utility function, which has previously not been feasible. We achieve this by
utilising Likelihood-Free Inference by Ratio Estimation (LFIRE) to approximate
posterior distributions, instead of the traditional approximate Bayesian
computation or synthetic likelihood methods. Secondly, we use Bayesian
optimisation in order to solve the optimal design problem, as opposed to the
typically used grid search or sampling-based methods. We find that this
increases efficiency and allows us to consider higher design dimensions.
