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Neural Importance Sampling for Rapid and Reliable Gravitational-Wave Inference
Maximilian Dax1, Stephen R Green2,3, Jonathan Gair2
1Max Planck Institute for Intelligent Systems, Max-Planck-Ring 4, 72076 Tübingen, Germany.
Physical Review Letters
|May 12, 2023
Summary
This study introduces a fast and accurate method for gravitational-wave inference using neural networks and importance sampling. The approach improves Bayesian posterior estimation and evidence calculation for cosmic event analysis.
Area of Science:
- Astrophysics and Cosmology
- Gravitational-Wave Astronomy
- Machine Learning in Science
Background:
- Gravitational-wave astronomy relies on complex Bayesian inference to analyze signals from cosmic events.
- Traditional inference methods can be computationally intensive, limiting the speed and scope of analysis.
- Deep learning offers potential for accelerating scientific inference but faces challenges in accuracy and verification.
Purpose of the Study:
- To develop a fast and accurate method for gravitational-wave inference by combining neural networks with importance sampling.
- To provide a robust framework for verifying and correcting deep learning-based posterior estimates in scientific applications.
- To enable unbiased Bayesian evidence estimation and improve the efficiency of gravitational-wave data analysis.
Main Methods:
- Amortized neural posterior estimation (NPE) is used to generate a rapid proposal distribution for Bayesian inference.
- Importance sampling is applied to re-weight the neural network's proposal, correcting for network inaccuracies.
- The method is validated on 42 binary black hole merger events using LIGO/Virgo data and advanced waveform models (SEOBNRv4PHM, IMRPhenomXPHM).
Main Results:
- Achieved a median sample efficiency of approximately 10%, representing a two-order-of-magnitude improvement over standard samplers.
- Demonstrated a tenfold reduction in the statistical uncertainty of the Bayesian evidence calculation.
- The approach provides a performance diagnostic (sample efficiency) and an unbiased estimate of the Bayesian evidence.
Conclusions:
- The combined neural posterior estimation and importance sampling method offers a significant advancement in gravitational-wave inference speed and accuracy.
- This technique addresses key criticisms of deep learning in scientific inference by providing verification and correction mechanisms.
- The approach is expected to have a substantial impact on gravitational-wave data analysis and serve as a paradigm for deep learning in science.
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