用于优化引力波探测、参数估计与天区定位的快速边缘化算法
Fast marginalization algorithm for optimizing gravitational wave detection, parameter estimation and sky localization
AI总结：
本文提出一种利用波形对外部参数的解析依赖、仅需一次波形求值即可快速边缘化似然的算法，可在单 CPU 核心约 50 毫秒内达到 10% 精度，并支持高阶模态、进动搜索、参数估计与低延迟天区定位。
摘要：
我们提出一种算法，用于对来自准圆轨道双星并合的引力波信号似然，就其外部参数进行边缘化，同时计入高次谐波和自旋诱导进动的影响。该算法以各个波形谐波相对于所有运行中探测器数据的匹配滤波时间序列，以及这些谐波的协方差作为输入。其输出是对描述并合时间、位置和取向的外部参数进行边缘化后的高斯似然，以及来自这些参数条件后验的样本。我们的算法利用波形对外部参数已知的解析依赖关系，仅通过一次波形求值即可高效地对其进行边缘化。当前实现在单个 CPU 核心上约 50 毫秒内即可使边缘化似然达到 10% 的精度，并通过 `cogwheel` 软件包公开发布。我们讨论了该工具在涉及高阶模态或进动的引力波搜索、高效且稳健的参数估计，以及为引力波警报的电磁跟进低延迟生成天区定位图方面的应用。纳入高阶模态可以改进距离测量，从而相较现有低延迟定位方法具备优势。
英文摘要：
We introduce an algorithm to marginalize the likelihood for a gravitational wave signal from a quasi-circular binary merger over its extrinsic parameters, accounting for the effects of higher harmonics and spin-induced precession. The algorithm takes as input the matched-filtering time series of individual waveform harmonics against the data in all operational detectors, and the covariances of the harmonics. The outputs are the Gaussian likelihood marginalized over extrinsic parameters describing the merger time, location and orientation, along with samples from the conditional posterior of these parameters. Our algorithm exploits the waveform's known analytical dependence on extrinsic parameters to efficiently marginalize over them using a single waveform evaluation. Our current implementation achieves a 10% precision on the marginalized likelihood within $\approx 50$ ms on a single CPU core and is publicly available through the package `cogwheel`. We discuss applications of this tool for gravitational wave searches involving higher modes or precession, efficient and robust parameter estimation, and generation of sky localization maps in low latency for electromagnetic followup of gravitational-wave alerts. The inclusion of higher modes can improve the distance measurement, providing an advantage over existing low-latency localization methods.
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