Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $d$-dimensional Sphere

Abstract

We propose an accelerated version of the holonomic gradient descent and apply it to calculating the maximum likelihood estimate (MLE) of the Fisher-Bingham distribution on a $d$-dimensional sphere. We derive a Pfaffian system (an integrable connection) and a series expansion associated with the normalizing constant with an error estimation. These enable us to solve some MLE problems up to dimension $d=7$ with a specified accuracy.

23 pages

Cited by in corpus (4)

• The Holonomic Rank of the Fisher-Bingham System of Differential Equations
• Pfaffian Systems of A-Hypergeometric Equations I: Bases of Twisted Cohomology Groups
• Calculation of orthant probabilities by the holonomic gradient method
• Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method