We review detection methods that are currently in use or have been proposed to search for a stochastic background of gravitational radiation. We consider both Bayesian and frequentist searches using ground-based and space-based laser interferometers, spacecraft Doppler tracking, and pulsar timing arrays; and we allow for anisotropy, non-Gaussianity, and non-standard polarization states. Our focus is on relevant data analysis issues, and not on the particular astrophysical or early Universe sources that might give rise to such backgrounds. We provide a unified treatment of these searches at the level of detector response functions, detection sensitivity curves, and, more generally, at the level of the likelihood function, since the choice of signal and noise models and prior probability distributions are actually what define the search. Pedagogical examples are given whenever possible to compare and contrast different approaches. We have tried to make the article as self-contained and comprehensive as possible, targeting graduate students and new researchers looking to enter this field.

我们回顾了目前正在使用或已提出的用于搜索引力辐射随机背景的检测方法。我们考虑使用地基和天基激光干涉仪、航天器多普勒跟踪和脉冲星计时阵列进行贝叶斯搜索和频率搜索；我们允许各向异性、非高斯性和非标准偏振态。我们的重点是相关的数据分析问题，而不是可能产生此类背景的特定天体物理学或早期宇宙来源。我们在检测器响应函数、检测灵敏度曲线级别以及更一般地在似然函数级别上对这些搜索进行统一处理，因为信号和噪声模型以及先验概率分布的选择实际上定义了搜索。只要有可能，就会给出教学例子来比较和对比不同的方法。我们试图使这篇文章尽可能独立和全面，针对希望进入该领域的研究生和新研究人员。