  Variational Bayesian Monte Carlo (VBMC) is a recently introduced framework
that uses Gaussian process surrogates to perform approximate Bayesian inference
in models with black-box, non-cheap likelihoods. In this work, we extend VBMC
to deal with noisy log-likelihood evaluations, such as those arising from
simulation-based models. We introduce new `global' acquisition functions, such
as expected information gain (EIG) and variational interquantile range (VIQR),
which are robust to noise and can be efficiently evaluated within the VBMC
setting. In a novel, challenging, noisy-inference benchmark comprising of a
variety of models with real datasets from computational and cognitive
neuroscience, VBMC+VIQR achieves state-of-the-art performance in recovering the
ground-truth posteriors and model evidence. In particular, our method vastly
outperforms `local' acquisition functions and other surrogate-based inference
methods while keeping a small algorithmic cost. Our benchmark corroborates VBMC
as a general-purpose technique for sample-efficient black-box Bayesian
inference also with noisy models.
