注意第二个间隙：间隙对噪声和信号参数推断的影响
Mind the second gap: The impact of gaps on noise and signal parameter inference
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中文总结 AI 辅助
本研究针对引力波数据处理中间隙导致的噪声误建模问题，提出解析与数值框架评估其对信号和噪声参数联合推断的影响，并给出精确时域似然求解方案。
中文摘要 AI 辅助
引力波数据在分析前总是需要经过某种条件处理：滤波和锥化操作以乘法方式作用于噪声，破坏了平稳性，而平稳性是Whittle似然（几乎所有引力波推断的基石）所依赖的前提。这个问题在LISA任务中尤为突出，因为间隙预计会与几乎所有信号重叠，且噪声必须与这些天体物理信号联合估计。我们提供了一个解析和数值框架，用于评估在存在间隙的情况下联合推断信号和噪声参数时噪声误建模的影响。基于Fisher矩阵形式（已通过贝叶斯推断验证），我们获得了模型不确定性、其最大似然估计以及后者真实离散度的闭式表达式，适用于各种似然近似。基于Fisher的线性形式通过Godambe-White曲率扩展到严重误建模所产生的非线性区域。我们调查了从长且良好锥化的中断到短且高频率的间隙家族，并注入了大质量黑洞双星系统。除了频繁间隙的情况外，我们展示了加窗协方差可以很好地由其主导对角线近似——即窗口与功率谱密度的卷积——用于估计信号和噪声参数。通过省略卷积，信号部分保持无偏，但噪声参数，特别是高频下占主导地位的光学计量噪声，在功率上被偏移超过一个数量级。在最高毛刺率下，对角线近似仍然准确，但精度损失了一个数量级。为解决此问题，我们提出了一种精确的时域似然方法，适用于幸存样本，并可通过预处理共轭梯度方法高效（且精确）求解。
英文摘要
Gravitational-wave data is never analysed without some conditioning: filtering and tapering act multiplicatively on the noise, destroying the stationarity on which the Whittle likelihood --- the backbone of nearly all gravitational-wave inference --- rests. The problem is particularly evident for LISA, where gaps are expected to overlap almost all signals and the noise must be estimated jointly with those astrophysical signals. We provide an analytical and numerical framework to assess the impact of noise mis-modelling when signal and noise parameters are inferred jointly in the presence of gaps. From a Fisher-matrix formalism verified against Bayesian inference, we obtain closed forms for the model uncertainties, their maximum-likelihood estimates and the true scatter in the latter, for various approximations to the likelihood. The Fisher-based linear formalism is extended through the Godambe--White curvature to the non-linear regime that severe mis-modelling produces. We survey gap families from long, well-tapered interruptions to short, high-rate ones, injecting massive black-hole binaries. Except in the case of frequent gaps, we show that the windowed covariance is well approximated by its leading diagonal --- the window convolved with the power spectral density --- for the estimation of both signal and noise parameters. By omitting the convolution, the signal sector remains unbiased but the noise parameters, in particular the optical-metrology noise which is dominant at high frequency, is displaced by over an order of magnitude in power. At the highest glitch rates the diagonal approximation stays accurate yet loses an order of magnitude in precision. To remedy this, we propose an exact time-domain likelihood of the surviving samples which can be efficiently (and accurately solved) via preconditioned conjugate gradient methods.
发表机构
- School of Physics and Astronomy, University of Glasgow（格拉斯哥大学物理与天文学学院）
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理学研究所（爱因斯坦研究所））
机构由 AI 辅助整理，请以论文原文为准。
