Mardia, K.V. orcid.org/0000-0003-0090-6235 (2025) Fisher’s legacy of directional statistics, and beyond to statistics on manifolds. Journal of Multivariate Analysis, 207. 105404. ISSN 0047-259X
Abstract
It is not an exaggeration to say that R.A. Fisher is the Albert Einstein of Statistics. He pioneered almost all the main branches of statistics, but it is not as well known that he opened the area of Directional Statistics with his 1953 paper introducing a distribution on the sphere which is now known as the Fisher distribution. He stressed that for spherical data one should take into account that the data is on a manifold. We will describe this Fisher distribution and reanalyze his geological data. We also comment on the two goals he set himself in that paper, and on how he reinvented the von Mises distribution on the circle. Since then, many extensions of this distribution have appeared bearing Fisher’s name such as the von Mises–Fisher distribution and the matrix Fisher distribution. In fact, the subject of Directional Statistics has grown tremendously in the last two decades with new applications emerging in life sciences, image analysis, machine learning and so on. We give a recent new method of constructing the Fisher type distributions on manifolds which has been motivated by some problems in machine learning. The number of directional distributions has increased since then, including the bivariate von Mises distribution and we describe its connection to work resulting in the 2024 Nobel-winning AlphaFold (in Chemistry). Further, the subject has evolved as Statistics on Manifolds which also includes the new field of Shape Analysis, and finally, we end with a historical note pointing out some correspondence between D’Arcy Thompson and R.A. Fisher related to Shape Analysis.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This is an author produced version of an article accepted for publication in Journal of Multivariate Analysis, made available under the terms of the Creative Commons Attribution License (CC-BY), which permits unrestricted use, distribution and reproduction in any medium, provided the original work is properly cited. |
Keywords: | Distributions on manifolds; Fisher distribution; Machine learning; Remanent magnetism; von Mises distribution; Wrapped tangent distributions |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Statistics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 06 Jan 2025 15:43 |
Last Modified: | 15 Jan 2025 14:36 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.jmva.2024.105404 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221296 |