# Properties and applications of Fisher distribution on the rotation group

@article{Sei2013PropertiesAA, title={Properties and applications of Fisher distribution on the rotation group}, author={Tomonari Sei and Hiroki Shibata and Akimichi Takemura and Katsuyoshi Ohara and Nobuki Takayama}, journal={J. Multivar. Anal.}, year={2013}, volume={116}, pages={440-455} }

## Tables from this paper

## 29 Citations

von Mises-Fisher distributions and their statistical divergence

- Mathematics
- 2022

The von Mises-Fisher family is a parametric family of distributions on the surface of the unit ball, summarised by a concentration parameter and a mean direction. As a quasiBayesian prior, the von…

Estimation of exponential-polynomial distribution by holonomic gradient descent

- Mathematics
- 2014

ABSTRACT We study the holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random…

3 Bayesian inference for the matrix Langevin distribution 3 . 1 The matrix Langevin distribution

- Computer Science, Mathematics
- 2013

A novel Markov chain Monte Carlo algorithm is developed to sample from this doubly intractable distribution of Stiefel manifold by mixing the matrix Langevin with respect to a random probability measure, which defines a flexible class of nonparametric models.

Interpretable Stein Goodness-of-fit Tests on Riemannian Manifold

- MathematicsICML
- 2021

This study develops goodness-of-fit testing and interpretable model criticism methods for general distributions on Riemannian manifolds, including those with an intractable normalization constant, based on extensions of kernel Stein discrepancy.

Bayesian Attitude Estimation With the Matrix Fisher Distribution on SO(3)

- MathematicsIEEE Transactions on Automatic Control
- 2018

Two types of intrinsic frameworks for Bayesian attitude estimation are constructed to avoid complexities or singularities of the attitude estimators developed in terms of quaternions.

On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method

- MathematicsStat. Comput.
- 2018

This work shows the explicit form of the Pfaffian equations using the expressions from Laplace inversion methods, which improves on the implementation of the holonomic algorithms for these problems and enables their adjustments for the degenerate cases.

On the exact maximum likelihood inference of Fisher–Bingham distributions using an adjusted holonomic gradient method

- Mathematics

Holonomic function theory has been successfully implemented in a series of recent papers to efficiently calculate the normalizing constant and perform likelihood estimation for the Fisher–Bingham…

The holonomic gradient method for the distribution function of the largest root of a Wishart matrix

- MathematicsJ. Multivar. Anal.
- 2013

Holonomic gradient descent for the Fisher–Bingham distribution on the $$d$$d-dimensional sphere

- MathematicsComput. Stat.
- 2014

An accelerated version of the holonomic gradient descent is proposed and a Pfaffian system and a series expansion associated with the normalizing constant with an error estimation are derived to solve some MLE problems up to dimension 7 with a specified accuracy.

Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method

- Mathematics, Computer ScienceStat. Comput.
- 2015

The holonomic gradient method is implemented to exactly compute the normalising constant of Bingham distributions and derives explicitly the Pfaffian system for this parametric case; the general approach for the maximum likelihood solution search is implemented and the method for degenerate cases is adjusted.

## References

SHOWING 1-10 OF 29 REFERENCES

Orientation Statistics Without Parametric Assumptions

- Business
- 1986

SUMMARY Maximum likelihood estimation using the matrix von Mises-Fisher distribution in orientation statistics leads to unacceptably complicated likelihood equations, essentially because of the…

ESTIMATION OF THE CONCENTRATION PARAMETERS OF THE FISHER MATRIX DISTRIBUTION ON 50(3) AND THE BINGHAM DISTRIBUTION ON Sq, q≥ 2

- Mathematics
- 1993

Summary
Two procedures are considered for estimating the concentration parameters of the Fisher matrix distribution for rotations or orientations in three dimensions. The first is maximum…

The holonomic gradient method for the distribution function of the largest root of a Wishart matrix

- MathematicsJ. Multivar. Anal.
- 2013

Aspects Of Multivariate Statistical Theory

- Mathematics
- 1982

Tables. Commonly Used Notation. 1. The Multivariate Normal and Related Distributions. 2. Jacobians, Exterior Products, Kronecker Products, and Related Topics. 3. Samples from a Multivariate Normal…

Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants

- Computer Science
- 2005

The numerical and theoretical results show that the first-order saddlepoint density approximation provides highly accurate approximations in a broad spectrum of cases.

Holonomic Gradient Descent and its Application to Fisher-Bingham Integral

- Mathematics, Computer ScienceAdv. Appl. Math.
- 2011

Systems of partial difierential equations for hypergeomet-ric functions of matrix argument

- Engineering
- 1970

A device for producing even distribution of a product dissolving in a current of water, such as a cake of chlorine serving to disinfect water in a swimming bath. The chlorine is contained in…

Using Algebraic Geometry

- Mathematics, Computer Science
- 1998

The Berlekamp-Massey-Sakata Decoding Algorithm is used for solving Polynomial Equations and for computations in Local Rings.

Risa/Asir—a computer algebra system

- Computer ScienceISSAC '92
- 1992

Risa’s subroutine libraries include basic arithmetic subroutines, parser, evaluator and storage manager, and each of them can be used individually.

Zonal Polynomials. Institute of Mathematical Statistics Lecture Notes—Monograph Series, 4

- Institute of Mathematical Statistics,
- 1984