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

DOI10.1007/s11222-017-9765-3zbMath1384.62172OpenAlexW2743201097WikidataQ59606437 ScholiaQ59606437MaRDI QIDQ1704019

Tomonari Sei, Alfred Kume

Publication date: 8 March 2018

Published in: Statistics and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11222-017-9765-3

zbMATH Keywords

holonomic functionsBingham distributionsdirectional statisticsFisher-Bingham distributions

Mathematics Subject Classification ID

Multivariate distribution of statistics (62H10) Directional data; spatial statistics (62H11) Point estimation (62F10)

Related Items (5)

Recent advances in directional statistics ⋮ Unnamed Item ⋮ The 8-parameter Fisher-Bingham distribution on the sphere ⋮ Spherical regression models with general covariates and anisotropic errors ⋮ Maximum likelihood estimation of the Fisher-Bingham distribution via efficient calculation of its normalizing constant

Uses Software

• hgm R

Cites Work

• Holonomic gradient method for distribution function of a weighted sum of noncentral chi-square random variables
• Properties and applications of Fisher distribution on the rotation group
• The holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• Holonomic gradient descent and its application to the Fisher-Bingham integral
• On the derivatives of the normalising constant of the Bingham distribution
• Holonomic gradient descent for the Fisher-Bingham distribution on the \(d\)-dimensional sphere
• The holonomic rank of the Fisher-Bingham system of differential equations
• Exact Bayesian inference for the Bingham distribution
• Gröbner Bases
• ESTIMATION OF THE CONCENTRATION PARAMETERS OF THE FISHER MATRIX DISTRIBUTION ON 50(3) AND THE BINGHAM DISTRIBUTION ON S_q, q≥ 2
• An Introduction to Numerical Analysis for Electrical and Computer Engineers
• Statistics of orthogonal axial frames
• Saddlepoint approximations for the Bingham and Fisher–Bingham normalising constants
• Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method
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