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.
@article{arxiv.1201.3239,
title = {Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $d$-dimensional Sphere},
author = {Tamio Koyama and Hiromasa Nakayama and Kenta Nishiyama and Nobuki Takayama},
journal= {arXiv preprint arXiv:1201.3239},
year = {2013}
}