利用无网格近似快速评估似然函数以重建致密双星源
Fast likelihood evaluation using meshfree approximations for reconstructing compact binary sources
AI总结：
本文提出一种结合数值线性代数与无网格插值的快速似然评估算法，可在几分钟内完成双中子星系统贝叶斯参数估计，结果与暴力计算统计一致，并有望推广至其他贝叶斯推断领域。
摘要：
最近，若干快速参数估计方法被提出，以应对地面引力波探测器网络在即将到来的科学运行中所探测到的致密双星源性质贝叶斯推断问题的计算挑战。其中一些方法经过良好优化，能够以多信使天文学所需的近实时方式重建引力波信号。在此背景下，本工作提出了一种新的、计算高效的算法，用于快速评估似然函数，该算法结合了数值线性代数与无网格插值方法。所提出的方法能够在样本空间的任意点快速评估似然函数，且精度损失可忽略不计，是网格化参数估计方案的一种替代方法。我们通过将快速似然评估方法与嵌套采样算法对接，获得了典型双中子星系统模型参数的后验样本。由这些样本得到的边缘化后验分布在统计上与暴力计算所得结果相同。我们发现，在探测到此类瞬变致密双星源后的几分钟内即可确定贝叶斯后验，从而提高利用不同波长望远镜对其进行及时后续观测的机会。本研究所提出的无网格技术蓝图有可能应用于其他领域的贝叶斯推断问题。
英文摘要：
Several rapid parameter estimation methods have recently been advanced to deal with the computational challenges of the problem of Bayesian inference of the properties of compact binary sources detected in the upcoming science runs of the terrestrial network of gravitational wave detectors. Some of these methods are well-optimized to reconstruct gravitational wave signals in nearly real-time necessary for multi-messenger astronomy. In this context, this work presents a new, computationally efficient algorithm for fast evaluation of the likelihood function using a combination of numerical linear algebra and mesh-free interpolation methods. The proposed method can rapidly evaluate the likelihood function at any arbitrary point of the sample space at a negligible loss of accuracy and is an alternative to the grid-based parameter estimation schemes. We obtain posterior samples over model parameters for a canonical binary neutron star system by interfacing our fast likelihood evaluation method with the nested sampling algorithm. The marginalized posterior distributions obtained from these samples are statistically identical to those obtained by brute force calculations. We find that such Bayesian posteriors can be determined within a few minutes of detecting such transient compact binary sources, thereby improving the chances of their prompt follow-up observations with telescopes at different wavelengths. It may be possible to apply the blueprint of the meshfree technique presented in this study to Bayesian inference problems in other domains.
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