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Bayesian experimental design (BED) is a framework that uses statisticalmodels and decision making under uncertainty to optimise the cost andperformance of a scientific experiment. Sequential BED, as opposed to staticBED, considers the scenario where we can sequentially update our beliefs aboutthe model parameters through data gathered in the experiment. A class of modelsof particular interest for the natural and medical sciences are implicitmodels, where the data generating distribution is intractable, but samplingfrom it is possible. Even though there has been a lot of work on static BED forimplicit models in the past few years, the notoriously difficult problem ofsequential BED for implicit models has barely been touched upon. We addressthis gap in the literature by devising a novel sequential design framework forparameter estimation that uses the Mutual Information (MI) between modelparameters and simulated data as a utility function to find optimalexperimental designs, which has not been done before for implicit models. Ourapproach uses likelihood-free inference by ratio estimation to simultaneouslyestimate posterior distributions and the MI. During the sequential BEDprocedure we utilise Bayesian optimisation to help us optimise the MI utility.We find that our framework is efficient for the various implicit models tested,yielding accurate parameter estimates after only a few iterations.

Sequential Bayesian Experimental Design for Implicit Models via Mutual Information