Robust and integrative Bayesian neural networks for likelihood-free parameter inference
This work addresses a specific bottleneck in likelihood-free inference for researchers in computational statistics, offering an incremental improvement over existing neural network-based methods.
The paper tackles the problem of simulation-based likelihood-free parameter inference by proposing a robust integrated approach that learns summary statistics using Bayesian neural networks and directly estimates posterior density, resulting in more efficient and robust convergence on large prior spaces.
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.