arXiv cs.AI· Siddhesh Kulkarni·· 13 小时前AI 评分18
圆与球面上的方向统计：看待数据的新角度
Directional Statistics on Circles and Spheres: A New Angle on Data
AI 导读
一篇 11 页的科普文章指出，两个靠近正北的罗盘方位取普通算术平均可能指向正南，因为角度分布在圆周而非直线上。文章借助真实风观测、扩散 MRI 方向数据和机器学习中的几何示例，介绍圆周与轴向平均、方向变异性以及圆和球面上的概率模型，核心原则是先识别观测数据的几何与对称性再选择统计方法。附 5 张图与可复现 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