# Elliptical Insights: Understanding Statistical Methods through Elliptical Geometry

arXiv: https://arxiv.org/abs/1302.4881 · HTML: https://mlsanity.com/paper/1302.4881/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2013.

## Built on by (most cited first, 5 of 5)

- [Estimating the Contamination Factor's Distribution in Unsupervised Anomaly Detection](https://mlsanity.com/paper/2210.10487/) (2022)
- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [Are Metrics Enough? Guidelines for Communicating and Visualizing Predictive Models to Subject Matter Experts](https://mlsanity.com/paper/2205.05749/) (2022)
- [VISPUR: Visual Aids for Identifying and Interpreting Spurious Associations in Data-Driven Decisions](https://mlsanity.com/paper/2307.14448/) (2023)
- [Rethinking Unsupervised Outlier Detection via Multiple Thresholding](https://mlsanity.com/paper/2407.05382/) (2024)

## Abstract (arXiv)

Visual insights into a wide variety of statistical methods, for both didactic and data analytic purposes, can often be achieved through geometric diagrams and geometrically based statistical graphs. This paper extols and illustrates the virtues of the ellipse and her higher-dimensional cousins for both these purposes in a variety of contexts, including linear models, multivariate linear models and mixed-effect models. We emphasize the strong relationships among statistical methods, matrix-algebraic solutions and geometry that can often be easily understood in terms of ellipses.