校准引力波参数的近似贝叶斯可信区间
Calibrating approximate Bayesian credible intervals of gravitational-wave parameters
AI总结：
本文提出一种利用自编码器和神经网络校准近似后验可信集的新方法，以提升引力波参数推断的统计覆盖，并在高质量双黑洞并合信号上验证了其对LISA等未来观测任务的适用性。
摘要：
在科学贝叶斯推断的实际应用中，近似方法被普遍采用，这往往出于便利，有时甚至是不得已而为之。在引力波数据分析领域，有时会使用计算速度快但属于近似的天体物理引力波信号波形模型来代替更精确的模型，以推断淹没在探测器噪声中的真实引力波信号的性质。此外，基于费舍尔信息的后验分布正态近似也可用于批量进行推断，而无需进行诸如马尔可夫链蒙特卡洛模拟等大量数值计算。这类近似通常会导致后验分布不准确，对真实后验的统计覆盖较差。在本文中，我们提出了一种新颖的校准程序，对一族近似后验分布的可信集进行校准，以确保其达到分析者指定水平下对真实后验的覆盖。我们的校准模型使用了自编码器和人工神经网络等工具来压缩数据（以提高效率）并执行逻辑回归等任务。作为原理验证，我们在高质量双黑洞并合产生的引力波信号上展示了我们的方法，该信号是近期未来天基引力波观测台LISA的一个有前景的波源。
英文摘要：
Approximations are commonly employed in realistic applications of scientific Bayesian inference, often due to convenience if not necessity. In the field of gravitational-wave (GW) data analysis, fast-to-evaluate but approximate waveform models of astrophysical GW signals are sometimes used in lieu of more accurate models to infer properties of a true GW signal buried within detector noise. In addition, a Fisher-information-based normal approximation to the posterior distribution can also be used to conduct inference in bulk, without the need for extensive numerical calculations such as Markov chain Monte Carlo (MCMC) simulations. Such approximations can generally lead to an inaccurate posterior distribution with poor statistical coverage of the true posterior. In this article, we present a novel calibration procedure that calibrates the credible sets for a family of approximate posterior distributions, to ensure coverage of the true posterior at a level specified by the analyst. Tools such as autoencoders and artificial neural networks are used within our calibration model to compress the data (for efficiency) and to perform tasks such as logistic regression. As a proof of principle, we demonstrate our formalism on the GW signal from a high-mass binary black hole merger, a promising source for the near-future space-based GW observatory LISA.
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