# Recent advances in directional statistics

arXiv: https://arxiv.org/abs/2005.06889 · HTML: https://mlsanity.com/paper/2005.06889/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 May 2020.

## Built on by (most cited first, 14 of 14)

- [Spherical Sliced-Wasserstein](https://mlsanity.com/paper/2206.08780/) (2022)
- [An Extension to Basis-Hypervectors for Learning from Circular Data in Hyperdimensional Computing](https://mlsanity.com/paper/2205.07920/) (2022)
- [Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning](https://mlsanity.com/paper/2407.16733/) (2024)
- [Single Image Estimation of Cell Migration Direction by Deep Circular Regression](https://mlsanity.com/paper/2406.19162/) (2024)
- [Deep learning joint extremes of metocean variables using the SPAR model](https://mlsanity.com/paper/2412.15808/) (2024)
- [Spherical Tree-Sliced Wasserstein Distance](https://mlsanity.com/paper/2503.11249/) (2025)
- [Principal subbundles for dimension reduction](https://mlsanity.com/paper/2307.03128/) (2023)
- [AlphaFold's Bayesian Roots in Probability Kinematics](https://mlsanity.com/paper/2505.19763/) (2025)
- [Weak Supervision in Analysis of News: Application to Economic Policy Uncertainty](https://mlsanity.com/paper/2209.05383/) (2022)
- [Bayesian Circular Regression with von Mises Quasi-Processes](https://mlsanity.com/paper/2406.13151/) (2024)
- [Reinforcement Learning in Hyperbolic Spaces: Models and Experiments](https://mlsanity.com/paper/2410.09466/) (2024)
- [Projected random forests and conformal prediction of circular data](https://mlsanity.com/paper/2410.24145/) (2024)
- [Synchronization-based clustering on the unit hypersphere](https://mlsanity.com/paper/2603.05067/) (2026)
- [Pose Tracking with a Foundation Pose Model and an Ensemble Directional Kalman Filter](https://mlsanity.com/paper/2605.03105/) (2026)

## Abstract (arXiv)

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 (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, aeronautics, 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 discussed.