Comment: 26 pages, 6 figuresRecent advances in computing power and the potential to make more realistic assumptions due to increased flexibility have led to the increased prevalence of simulation models in economics. While models of this class, and particularly agent-based models, are able to replicate a number of empirically-observed stylised facts not easily recovered by more traditional alternatives, such models remain notoriously difficult to estimate due to their lack of tractable likelihood functions. While the estimation literature continues to grow, existing attempts have approached the problem primarily from a frequentist perspective, with the Bayesian estimation literature remaining comparatively less developed. For this reason, we introduce a Bayesian estimation protocol that makes use of deep neural networks to construct an approximation to the likelihood, which we then benchmark against a prominent alternative from the existing literature. Overall, we find that our proposed methodology consistently results in more accurate estimates in a variety of settings, including the estimation of financial heterogeneous agent models and the identification of changes in dynamics occurring in models incorporating structural breaks.