Properties and applications of Fisher distribution on the rotation group

Tomonari Sei, Hiroki Shibata, Akimichi Takemura, Katsuyoshi Ohara, Nobuki Takayama

研究成果: Article査読

21 被引用数 (Scopus)

抄録

We study properties of Fisher distribution (von Mises-Fisher distribution, matrix Langevin distribution) on the rotation group SO(3). In particular we apply the holonomic gradient descent, introduced by Nakayama et al. (2011) [16], and a method of series expansion for evaluating the normalizing constant of the distribution and for computing the maximum likelihood estimate. The rotation group can be identified with the Stiefel manifold of two orthonormal vectors. Therefore from the viewpoint of statistical modeling, it is of interest to compare Fisher distributions on these manifolds. We illustrate the difference with an example of near-earth objects data.

本文言語English
ページ(範囲)440-455
ページ数16
ジャーナルJournal of Multivariate Analysis
116
DOI
出版ステータスPublished - 2013 4月
外部発表はい

ASJC Scopus subject areas

  • 統計学および確率
  • 数値解析
  • 統計学、確率および不確実性

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