The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, [Formula: see text]-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

中文翻译：

---

引力波数据分析。形式主义和示例应用：高斯案例。

本文回顾了信号检测的统计理论在探测器噪声中分析确定性引力波信号的应用。提出了信号检测和参数估计理论的统计基础。介绍了最佳数据分析方法的理论评估及其实际实施所需的几种工具。它们包括最佳信噪比、Fisher 矩阵、误报和检测概率、[公式：参见文本]统计、模板放置和拟合因子。这些工具适用于信号埋藏在平稳和高斯噪声中的情况。讨论了有效实施最佳数据分析技术的算法。给出了一般引力波信号的公式，其中包括作为特殊情况的大多数感兴趣的确定性信号。