Holonomic gradient descent for the Fisher–Bingham distribution on the $$d$$ d -dimensional sphere

Tamio Koyama (), Hiromasa Nakayama, Kenta Nishiyama and Nobuki Takayama

Computational Statistics, 2014, vol. 29, issue 3, 683 pages

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 $$d$$ 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 $$d=7$$ d = 7 with a specified accuracy. Copyright Springer-Verlag Berlin Heidelberg 2014

Keywords: Fisher–Bingham distribution; Maximum likelihood estimate; Holonomic gradient descent; Integrable connection; Pfaffian system (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:compst:v:29:y:2014:i:3:p:661-683

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DOI: 10.1007/s00180-013-0456-z

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