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

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

2012-01-16

arxiv.org/abs/1201.3239v1

Mathematics

Statistics Theory

16 pages

Scientific paper

We apply the holonomic gradient descent recently introduced in [7] to the
maximal likelihood estimate (MLE) with respect to the Fisher-Bingham
distribution on the $n$-dimensional sphere. We derive an integrable connection
(a Pfaffian system) and a series expansion associated to the normalization
constant. These enable us to solve some MLE problems up to $n=7$.

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