The past two decades have seen a major expansion in the availability, size, and precision of time-domain data sets in astronomy. Owing to their unique combination of flexibility, mathematical simplicity, and comparative robustness, Gaussian processes (GPs) have emerged recently as the solution of choice to model stochastic signals in such data sets. In this review, we provide a brief introduction to the emergence of GPs in astronomy, present the underlying mathematical theory, and give practical advice considering the key modeling choices involved in GP regression. We then review applications of GPs to time-domain data sets in the astrophysical literature so far, from exoplanets to active galactic nuclei, showcasing the power and flexibility of the method. We provide worked examples using simulated data, with links to the source code; discuss the problem of computational cost and scalability; and give a snapshot of the current ecosystem of open-source GP software packages. In summary: ▪ GP regression is a conceptually simple but statistically principled and powerful tool for the analysis of astronomical time series. ▪ It is already widely used in some subfields, such as exoplanets, and gaining traction in many others, such as optical transients. ▪ Driven by further algorithmic and conceptual advances, we expect that GPs will continue to be an important tool for robust and interpretable time-domain astronomy for many years to come.

中文翻译：

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天文时间序列的高斯过程回归


在过去的二十年里，天文学中时域数据集的可用性、规模和精度有了重大扩展。由于高斯过程 (GP) 具有灵活性、数学简单性和相对鲁棒性的独特组合，最近已成为此类数据集中随机信号建模的首选解决方案。在这篇综述中，我们简要介绍了天文学中 GP 的出现，介绍了基础数学理论，并考虑了 GP 回归中涉及的关键建模选择，给出了实用建议。然后，我们回顾了迄今为止天体物理学文献中 GP 在时域数据集上的应用，从系外行星到活动星系核，展示了该方法的强大功能和灵活性。我们提供使用模拟数据的工作示例，以及源代码的链接；讨论计算成本和可扩展性问题；并简要介绍当前开源 GP 软件包生态系统。总结： ▪ GP 回归是一个概念简单但具有统计学原理的强大工具，用于分析天文时间序列。 ▪ 它已广泛应用于某些子领域（例如系外行星），并在许多其他领域（例如光瞬变）获得关注。 ▪ 在算法和概念进一步进步的推动下，我们预计全球定位系统将在未来许多年内继续成为稳健且可解释的时域天文学的重要工具。