Properties and applications of Fisher distribution on the rotation group

JOURNAL OF MULTIVARIATE ANALYSIS

卷:116

Article

Sei, Tomonari¹  Shibata, Hiroki²  Takemura, Akimichi^2,3  Ohara, Katsuyoshi⁴  Takayama, Nobuki^3,5 

[1] Keio Univ, Dept Math, Tokyo 108, Japan

[2] Univ Tokyo, Grad Sch Informat Sci & Technol, Dept Math Informat, Tokyo 1138654, Japan

[3] CREST, JST, Tokyo, Japan

[4] Kanazawa Univ, Fac Math & Phys, Kanazawa, Ishikawa 9201192, Japan

[5] Kobe Univ, Dept Math, Kobe, Hyogo, Japan

关键词: Algebraic statistics;    Directional statistics;    Holonomic gradient descent;    Maximum likelihood estimation;    Rotation group;   

DOI  :  10.1016/j.jmva.2013.01.010

来源: Elsevier

【 摘 要 】

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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free