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

2012/01/16 by Koyama, Tamio, Nakayama, Hiromasa, Nishiyama, Kenta +1
#16Z99 #32C38 #33F10 #62F10 #90C52 #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1201.3239

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.

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