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.

翻译：我们将摊销神经后验估计与重要性采样相结合，以实现快速且精确的引力波推断。首先利用神经网络生成贝叶斯后验的快速提议分布，随后根据潜在似然函数和先验分布附加重要性权重。这提供了：(1) 经校正且免受网络误差影响的后验分布；(2) 用于评估提议分布并识别失效案例的性能诊断指标（样本效率）；(3) 贝叶斯证据的无偏估计。通过建立这种独立验证与校正机制，我们回应了针对深度学习用于科学推断的最常见批评。我们开展了一项大型研究，使用SEOBNRv4PHM和IMRPhenomXPHM波形模型分析了LIGO与Virgo观测到的42个双黑洞并合事件。结果显示中位样本效率约为10%（比标准采样器高两个数量级），且对数证据的统计不确定性降低了十倍。基于这些优势，我们预计该方法将对引力波推断产生重大影响，并成为在科学应用中利用深度学习方法的范式。