# Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference

arXiv: https://arxiv.org/abs/2210.05686 · HTML: https://mlsanity.com/paper/2210.05686/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 74 references that are in the map.
- First posted on arXiv 11 Oct 2022.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Real-time gravitational-wave science with neural posterior estimation](https://mlsanity.com/paper/2106.12594/) (2021)
- [Fast ε-free Inference of Simulation Models with Bayesian Conditional Density Estimation](https://mlsanity.com/paper/1605.06376/) (2016)
- [Investigating the Impact of Model Misspecification in Neural Simulation-based Inference](https://mlsanity.com/paper/2209.01845/) (2022)
- [Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy](https://mlsanity.com/paper/1909.06296/) (2019)
- [Complete parameter inference for GW150914 using deep learning](https://mlsanity.com/paper/2008.03312/) (2020)
- [Inference Networks for Sequential Monte Carlo in Graphical Models](https://mlsanity.com/paper/1602.06701/) (2016)
- [Gravitational-wave parameter estimation with autoregressive neural network flows](https://mlsanity.com/paper/2002.07656/) (2020)
- [Lightning-Fast Gravitational Wave Parameter Inference through Neural Amortization](https://mlsanity.com/paper/2010.12931/) (2020)
- [Group equivariant neural posterior estimation](https://mlsanity.com/paper/2111.13139/) (2021)
- [alpha-Deep Probabilistic Inference (alpha-DPI): efficient uncertainty quantification from exoplanet astrometry to black hole feature extraction](https://mlsanity.com/paper/2201.08506/) (2022)
- [Swift sky localization of gravitational waves using deep learning seeded importance sampling](https://mlsanity.com/paper/2111.00833/) (2021)

## Built on by (most cited first, 28 of 28)

- [Flow Matching for Scalable Simulation-Based Inference](https://mlsanity.com/paper/2305.17161/) (2023)
- [Simulation-Based Inference: A Practical Guide](https://mlsanity.com/paper/2508.12939/) (2025)
- [Consistency Models for Scalable and Fast Simulation-Based Inference](https://mlsanity.com/paper/2312.05440/) (2023)
- [Real-time gravitational-wave inference for binary neutron stars using machine learning](https://mlsanity.com/paper/2407.09602/) (2024)
- [Sensitivity-Aware Amortized Bayesian Inference](https://mlsanity.com/paper/2310.11122/) (2023)
- [Diffusion posterior sampling for simulation-based inference in tall data settings](https://mlsanity.com/paper/2404.07593/) (2024)
- [Adversarial robustness of amortized Bayesian inference](https://mlsanity.com/paper/2305.14984/) (2023)
- [SciTS: Scientific Time Series Understanding and Generation with LLMs](https://mlsanity.com/paper/2510.03255/) (2025)
- [Leveraging Self-Consistency for Data-Efficient Amortized Bayesian Inference](https://mlsanity.com/paper/2310.04395/) (2023)
- [Cost-aware simulation-based inference](https://mlsanity.com/paper/2410.07930/) (2024)
- [Adapting to noise distribution shifts in flow-based gravitational-wave inference](https://mlsanity.com/paper/2211.08801/) (2022)
- [Inferring Atmospheric Properties of Exoplanets with Flow Matching and Neural Importance Sampling](https://mlsanity.com/paper/2312.08295/) (2023)
- [Demonstrating the power and flexibility of variational assumptions for amortized neural posterior estimation in environmental applications](https://mlsanity.com/paper/2404.10899/) (2024)
- [Fast and Reliable Probabilistic Reflectometry Inversion with Prior-Amortized Neural Posterior Estimation](https://mlsanity.com/paper/2407.18648/) (2024)
- [Amortized Bayesian Workflow](https://mlsanity.com/paper/2409.04332/) (2024)
- [nbi: the Astronomer's Package for Neural Posterior Estimation](https://mlsanity.com/paper/2312.03824/) (2023)
- [Conditional neural control variates for variance reduction in Bayesian inverse problems](https://mlsanity.com/paper/2602.21357/) (2026)
- [Scalable Simulation-Based Model Inference with Test-Time Complexity Control](https://mlsanity.com/paper/2603.15292/) (2026)
- [Accelerated Bayesian parameter estimation and model selection for gravitational waves with normalizing flows](https://mlsanity.com/paper/2410.21076/) (2024)
- [Synthesizing 3D Abstractions by Inverting Procedural Buildings with Transformers](https://mlsanity.com/paper/2501.17044/) (2025)
- [Discriminative versus Generative Approaches to Simulation-based Inference](https://mlsanity.com/paper/2503.07962/) (2025)
- [Flexible Gravitational-Wave Parameter Estimation with Transformers](https://mlsanity.com/paper/2512.02968/) (2025)
- [An Introduction to Bayesian and Frequentist Simulation-Based Inference with Machine Learning](https://mlsanity.com/paper/2607.21702/) (2026)
- [Recent Advances in Simulation-based Inference for Gravitational Wave Data Analysis](https://mlsanity.com/paper/2507.11192/) (2025)
- [Misspecification-robust amortised simulation-based inference using variational methods](https://mlsanity.com/paper/2509.05724/) (2025)
- [STEP: Scientific Time-Series Encoder Pretraining via Cross-Domain Distillation](https://mlsanity.com/paper/2603.18688/) (2026)
- [Neural Posterior Estimation for Stochastic Epidemic Models Using Final Outcome Data](https://mlsanity.com/paper/2606.02874/) (2026)
- [Fast, accurate, and differentiable: a neural-network surrogate for NRSur7dq4 precessing binary black hole waveforms](https://mlsanity.com/paper/2607.24960/) (2026)

## Abstract (arXiv)

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 ≈ 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.