Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere, and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper, we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (Wiley 1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, space situational awareness, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments are discussed.

主流统计方法通常适用于在欧几里得空间中观测到的数据。但是，在许多具有重大科学意义的环境中，正在考虑的数据的自然支撑是黎曼流形，例如单位圆，圆环，球体及其扩展。通常，可以使用一个或多个方向来表示此类数据，方向统计信息是处理其分析的统计信息的分支。在本文中，我们回顾了自Mardia和Jupp出版以来（Wiley，1999年）该领域的许多最新进展，该领域仍然是定向统计方面最全面的文本。在许多领域，诸如天文学，医学，遗传学，神经病学，空间态势感知，声学，图像分析，文本挖掘，环境计量学和机器学习。首先，我们将研究方向数据探索性分析的发展，然后再发展为分布模型，推理的一般方法，假设检验，回归，非参数曲线估计，降维，分类和聚类的方法以及时间序列，空间和模型的建模时空数据。还提供了用于分析方向数据的当前可用软件的概述，并讨论了潜在的未来发展。降维，分类和聚类的方法，以及时间序列，空间和时空数据的建模方法。还提供了用于分析方向数据的当前可用软件的概述，并讨论了潜在的未来发展。降维，分类和聚类的方法，以及时间序列，空间和时空数据的建模方法。还提供了用于分析方向数据的当前可用软件的概述，并讨论了潜在的未来发展。