AI 中文总结
针对LISA探测SGWB的噪声与信号重叠难题，提出贝叶斯框架，对比幂律与样条信号模型，发现样条模型可恢复局域特征，强先验能降低低频简并性，揭示模型灵活性的权衡关系。
AI 中文摘要
探测随机引力波背景（SGWB）是激光干涉空间天线（LISA）的主要科学目标。然而，由于信号和仪器噪声均为随机且在毫赫兹波段重叠，提取这些信号十分困难。本研究提出一种贝叶斯框架，用于联合估计LISA的噪声与SGWB信号。该方法采用灵活的对数惩罚样条对LISA仪器噪声建模，通过粗糙度惩罚防止过拟合，同时保持计算效率；对于SGWB，我们对比幂律模型与基于样条的模型，研究信号模型和噪声先验的选择对信号恢复与探测的影响。利用模拟LISA数据，我们发现当信号符合假设形状时，幂律模型能给出更紧凑的估计，但无法恢复幂律未描述的局域频谱特征，导致信号被仪器噪声样条吸收；而全基于样条的模型限制更少，可成功恢复此类特征。我们还发现，关于测试质量噪声的更强先验信息有助于减少低频下噪声与SGWB模型的简并性，提升信号探测能力。这些结果体现了一个权衡：当假设的信号形状正确时，增加模型灵活性会降低灵敏度；当信号形状不正确时，模型灵活性可防止偏差。
英文摘要
The detection of a stochastic gravitational-wave background (SGWB) is a primary science objective for the Laser Interferometer Space Antenna (LISA). However, extracting these signals is difficult because both the signal and the instrumental noise are stochastic and overlapping in the millihertz band. In this work, we present a Bayesian framework for the joint estimation of LISA noise and SGWB signals. Our approach models the LISA instrumental noise using flexible log-penalized splines, employing a roughness penalty to prevent overfitting while maintaining computational efficiency. For the SGWB, we compare a power-law model with a spline-based model and study how the choice of signal model and noise prior affects signal recovery and detection. Using simulated LISA data, we find that the power-law model gives tighter estimates when the signal follows the assumed shape. However, it fails to recover a localized spectral feature that is not described by a power law, causing the signal to be absorbed by the instrumental-noise spline. The fully spline-based model is less restrictive and successfully recovers such features. We also find that stronger prior information about the test-mass noise helps reduce the degeneracy between the noise and SGWB models at low frequencies, improving signal detection. These results reflect a single trade-off: added model flexibility reduces sensitivity when the assumed signal shape is correct, and prevents bias when it is not.
