圆与球上的方向统计：看待数据的新角度
Directional Statistics on Circles and Spheres: A New Angle on Data
AI 导读
arXiv 上一篇 11 页的讲解性文章介绍圆形与轴向平均、方向变异性及圆与球面上的概率模型，指出两个接近北的罗盘方位角用普通算术平均可能指向南，因为角度分布在圆上而非直线。文章用真实风速观测、扩散 MRI 方向和机器学习几何例子说明方法选择应先识别观测数据的几何与对称性，并附可复现的 R 代码。
正文 · 原文
Abstract:Two compass bearings near north can have an ordinary arithmetic mean pointing south: the difficulty is that angles live on a circle, not a straight line. Using real wind observations, diffusion-MRI orientations, and geometric examples from machine learning, this article introduces circular and axial averages, directional variability, and probability models on circles and spheres. The guiding principle is to identify the geometry and symmetries of the observations before choosing a statistical method.
| Comments: | 11 pages, 5 figures. Expository article with real-data examples and reproducible R code. Submitted to Resonance: Journal of Science Education |
| Subjects: | Methodology (stat.ME); Artificial Intelligence (cs.AI); Machine Learning (stat.ML) |
| MSC classes: | 62H11 |
| Cite as: | arXiv:2610.36227 [stat.ME] |
| (or arXiv:2610.36227v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2610.36227 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Siddhesh Kulkarni [view email]
[v1]
Mon, 26 Oct 2026 20:05:24 UTC (99 KB)
来源：arXiv cs.AI · arxiv.org