  Approximate Bayesian Computation (ABC) provides methods for Bayesian
inference in simulation-based stochastic models which do not permit tractable
likelihoods. We present a new ABC method which uses probabilistic neural
emulator networks to learn synthetic likelihoods on simulated data -- both
local emulators which approximate the likelihood for specific observed data, as
well as global ones which are applicable to a range of data. Simulations are
chosen adaptively using an acquisition function which takes into account
uncertainty about either the posterior distribution of interest, or the
parameters of the emulator. Our approach does not rely on user-defined
rejection thresholds or distance functions. We illustrate inference with
emulator networks on synthetic examples and on a biophysical neuron model, and
show that emulators allow accurate and efficient inference even on
high-dimensional problems which are challenging for conventional ABC
approaches.
