Properties and applications of Fisher distribution on the rotation group

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

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

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
Volume116
DOIs
Publication statusPublished - 2013 Apr

Fingerprint

Rotation Group
Maximum likelihood
Von Mises-Fisher Distribution
Earth (planet)
Stiefel Manifold
Normalizing Constant
Statistical Modeling
Gradient Descent
Orthonormal
Maximum Likelihood Estimate
Series Expansion
Computing

Keywords

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

ASJC Scopus subject areas

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

Cite this

Properties and applications of Fisher distribution on the rotation group. / Sei, Tomonari; Shibata, Hiroki; Takemura, Akimichi; Ohara, Katsuyoshi; Takayama, Nobuki.

In: Journal of Multivariate Analysis, Vol. 116, 04.2013, p. 440-455.

Research output: Contribution to journalArticle

Sei, Tomonari ; Shibata, Hiroki ; Takemura, Akimichi ; Ohara, Katsuyoshi ; Takayama, Nobuki. / Properties and applications of Fisher distribution on the rotation group. In: Journal of Multivariate Analysis. 2013 ; Vol. 116. pp. 440-455.
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