Properties and applications of Fisher distribution on the rotation group

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

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)440-455
Number of pages16
JournalJournal of Multivariate Analysis
Publication statusPublished - 2013 Apr
Externally publishedYes


  • Algebraic statistics
  • Directional statistics
  • Holonomic gradient descent
  • Maximum likelihood estimation
  • Rotation group

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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