Directional Statistics with the Spherical Normal Distribution

Søren Hauberg*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingArticle in proceedingsResearchpeer-review

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Abstract

A well-known problem in directional statistics - the study of data distributed on the unit sphere - is that current models disregard the curvature of the underlying sample space. This ensures computationally efficiency, but can influence results. To investigate this, we develop efficient inference techniques for data distributed by the curvature-aware spherical normal distribution. We derive closed-form expressions for the normalization constant when the distribution is isotropic, and a fast and accurate approximation for the anisotropic case on the two-sphere. We further develop approximate posterior inference techniques for the mean and concentration of the distribution, and propose a fast sampling algorithm for simulating the distribution. Combined, this provides the tools needed for practical inference on the unit sphere in a manner that respects the curvature of the underlying sample space.

Original languageEnglish
Title of host publicationProceedings of 2018 21st International Conference on Information Fusion, FUSION 2018
PublisherIEEE
Publication date5 Sep 2018
Pages704-711
ISBN (Print)9780996452762
DOIs
Publication statusPublished - 5 Sep 2018
Event2018 21st International Conference on Information Fusion - Cambridge , United Kingdom
Duration: 10 Jul 201813 Jul 2018

Conference

Conference2018 21st International Conference on Information Fusion
CountryUnited Kingdom
CityCambridge
Period10/07/201813/07/2018

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