Likelihood-free inference with emulator networks

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.