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

TL;DR

This paper introduces a robust Bayesian neural network approach for likelihood-free parameter inference, improving efficiency and accuracy by incorporating uncertainty and adaptive sampling.

Contribution

It presents a novel integrated Bayesian neural network method that directly estimates posterior densities and uses adaptive sampling for better convergence.

Findings

Outperforms existing methods on benchmark examples

Provides more robust and efficient convergence

Incorporates prediction uncertainty into likelihood-free inference

Abstract

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.