  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 require density estimation as a post-processing
step building upon 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
directly estimates the posterior density using categorical distributions. An
adaptive sampling scheme selects simulation locations to efficiently and
iteratively refine the predictive posterior of the network conditioned on
observations. This allows for more efficient and robust convergence on
comparatively large prior spaces. We demonstrate our approach on benchmark
examples and compare against related methods.
