Properties and applications of Fisher distribution on the rotation group

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

doi:10.1016/j.jmva.2013.01.010

Properties and applications of Fisher distribution on the rotation group

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

Research output: Contribution to journal › Article › peer-review

23 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 language	English
Pages (from-to)	440-455
Number of pages	16
Journal	Journal of Multivariate Analysis
Volume	116
DOIs	https://doi.org/10.1016/j.jmva.2013.01.010
Publication status	Published - 2013 Apr
Externally published	Yes

Keywords

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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10.1016/j.jmva.2013.01.010

Cite this

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title = "Properties and applications of Fisher distribution on the rotation group",

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.",

keywords = "Algebraic statistics, Directional statistics, Holonomic gradient descent, Maximum likelihood estimation, Rotation group",

author = "Tomonari Sei and Hiroki Shibata and Akimichi Takemura and Katsuyoshi Ohara and Nobuki Takayama",

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doi = "10.1016/j.jmva.2013.01.010",

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AU - Sei, Tomonari

AU - Shibata, Hiroki

AU - Takemura, Akimichi

AU - Ohara, Katsuyoshi

AU - Takayama, Nobuki

PY - 2013/4

Y1 - 2013/4

N2 - 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.

AB - 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.

KW - Algebraic statistics

KW - Directional statistics

KW - Holonomic gradient descent

KW - Maximum likelihood estimation

KW - Rotation group

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JO - Journal of Multivariate Analysis

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ER -

Properties and applications of Fisher distribution on the rotation group

Abstract

Keywords

ASJC Scopus subject areas

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