This survey is devoted to recent developments in the statistical analysis of spherical data, with a view to applications in Cosmology. We will start from a brief discussion of Cosmological questions and motivations, arguing that most Cosmological observables are spherical random fields. Then, we will introduce some mathematical background on spherical random fields, including spectral representations and the construction of needlet and wavelet frames. We will then focus on some specific issues, including tools and algorithms for map reconstruction (\textit{i.e.}, separating the different physical components which contribute to the observed field), geometric tools for testing the assumptions of Gaussianity and isotropy, and multiple testing methods to detect contamination in the field due to point sources. Although these tools are introduced in the Cosmological context, they can be applied to other situations dealing with spherical data. Finally, we will discuss more recent and challenging issues such as the analysis of polarization data, which can be viewed as realizations of random fields taking values in spin fiber bundles.

翻译：本文综述了球面数据统计分析的最新进展，重点关注其在宇宙学中的应用。首先简要讨论宇宙学问题与动机，论证宇宙学可观测量的本质多为球面随机场。随后介绍球面随机场的数学基础，包括谱表示以及needlet与小波框架的构建方法。在此基础上，聚焦若干关键问题：用于地图重建的工具与算法（即分离构成观测场的不同物理成分）、检验高斯性与各向同性假设的几何工具，以及用于检测点源污染的多元检验方法。尽管这些工具源自宇宙学背景，但可推广至其他涉及球面数据的场景。最后，探讨更具前沿性的挑战，例如极化数据分析——这类数据可视为自旋纤维丛上取值的随机场实现。