Misspecification-robust likelihood-free inference in high dimensions

Likelihood-free inference for simulator-based statistical models has developed rapidly from its infancy to a useful tool for practitioners. However, models with more than a handful of parameters still generally remain a challenge for the Approximate Bayesian Computation (ABC) based inference. To advance the possibilities for performing likelihood-free inference in higher dimensional parameter spaces, we introduce an extension of the popular Bayesian optimisation based approach to approximate discrepancy functions in a probabilistic manner which lends itself to an efficient exploration of the parameter space. Our approach achieves computational scalability for higher dimensional parameter spaces by using separate acquisition functions, discrepancies, and associated summary statistics for distinct subsets of the parameters. The efficient additive acquisition structure is combined with exponentiated loss-likelihood to provide a misspecification-robust characterisation of posterior distributions for subsets of model parameters. The method successfully performs computationally efficient inference in a moderately sized parameter space and compares favourably to existing modularised ABC methods. We further illustrate the potential of this approach by fitting a bacterial transmission dynamics model to a real data set, which provides biologically coherent results on strain competition in a 30-dimensional parameter space.