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Data collection is a critical step in statistical inference and data science,and the goal of statistical experimental design (ED) is to find the datacollection setup that can provide most information for the inference. In thiswork we consider a special type of ED problems where the likelihoods are notavailable in a closed form. In this case, the popular information-theoreticKullback-Leibler divergence (KLD) based design criterion can not be useddirectly, as it requires to evaluate the likelihood function. To address theissue, we derive a new utility function, which is a lower bound of the originalKLD utility. This lower bound is expressed in terms of the summation of two ormore entropies in the data space, and thus can be evaluated efficiently viaentropy estimation methods. We provide several numerical examples todemonstrate the performance of the proposed method.

An approximate KLD based experimental design for models with intractable likelihoods