Robust and integrative Bayesian neural networks for likelihood-free parameter inference

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches for learning summarizing networks are mainly based on deterministic neural networks, and do not take network prediction uncertainty into account. This work proposes a robust integrated approach that learns summary statistics using Bayesian neural networks, and produces a proposal posterior density using categorical distributions. An adaptive sampling scheme selects simulation locations to efficiently and iteratively refine the predictive proposal posterior of the network conditioned on observations. This allows for more efficient and robust convergence on comparatively large prior spaces. The approximated proposal posterior can then either be processed through a correction mechanism, or be used in conjunction with a density estimator to arrive at the true posterior. We demonstrate our approach on benchmark examples.