  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 and
discrepancies for each parameter. The efficient additive acquisition structure
is combined with exponentiated loss -likelihood to provide a
misspecification-robust characterisation of the marginal posterior distribution
for all model parameters. The method successfully performs computationally
efficient inference in a 100-dimensional space on canonical examples 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.
