Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference

TL;DR

This paper introduces a neural importance sampling method that accelerates and improves the accuracy of gravitational-wave parameter inference, providing reliable results with fewer samples and enabling effective scientific analysis.

Contribution

It combines neural posterior estimation with importance sampling to produce unbiased, efficient, and diagnostic-enabled gravitational-wave inference, addressing key criticisms of deep learning in science.

Findings

Median sample efficiency of ~10% (10x better than standard methods)

Ten-fold reduction in statistical uncertainty of log evidence

Successful analysis of 42 LIGO/Virgo black hole mergers

Abstract

We combine amortized neural posterior estimation with importance sampling for fast and accurate gravitational-wave inference. We first generate a rapid proposal for the Bayesian posterior using neural networks, and then attach importance weights based on the underlying likelihood and prior. This provides (1) a corrected posterior free from network inaccuracies, (2) a performance diagnostic (the sample efficiency) for assessing the proposal and identifying failure cases, and (3) an unbiased estimate of the Bayesian evidence. By establishing this independent verification and correction mechanism we address some of the most frequent criticisms against deep learning for scientific inference. We carry out a large study analyzing 42 binary black hole mergers observed by LIGO and Virgo with the SEOBNRv4PHM and IMRPhenomXPHM waveform models. This shows a median sample efficiency of $\approx 10\%$ (two orders-of-magnitude better than standard samplers) as well as a ten-fold reduction in the statistical uncertainty in the log evidence. Given these advantages, we expect a significant impact on gravitational-wave inference, and for this approach to serve as a paradigm for harnessing deep learning methods in scientific applications.