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State-of-the-art neural network-based methods for learning summary statisticshave delivered promising results for simulation-based likelihood-free parameterinference. Existing approaches require density estimation as a post-processingstep building upon deterministic neural networks, and do not take networkprediction uncertainty into account. This work proposes a robust integratedapproach that learns summary statistics using Bayesian neural networks, anddirectly estimates the posterior density using categorical distributions. Anadaptive sampling scheme selects simulation locations to efficiently anditeratively refine the predictive posterior of the network conditioned onobservations. This allows for more efficient and robust convergence oncomparatively large prior spaces. We demonstrate our approach on benchmarkexamples and compare against related methods.

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