  Simulation-based inference techniques are indispensable for parameter
estimation of mechanistic and simulable models with intractable likelihoods.
While traditional statistical approaches like approximate Bayesian computation
and Bayesian synthetic likelihood have been studied under well-specified and
misspecified settings, they often suffer from inefficiencies due to wasted
model simulations. Neural approaches, such as sequential neural likelihood
(SNL) avoid this wastage by utilising all model simulations to train a neural
surrogate for the likelihood function. However, the performance of SNL under
model misspecification is unreliable and can result in overconfident posteriors
centred around an inaccurate parameter estimate. In this paper, we propose a
novel SNL method, which through the incorporation of additional adjustment
parameters, is robust to model misspecification and capable of identifying
features of the data that the model is not able to recover. We demonstrate the
efficacy of our approach through several illustrative examples, where our
method gives more accurate point estimates and uncertainty quantification than
SNL.
