Holonomic gradient descent for the Fisher–Bingham distribution on the \(d\)-dimensional sphere
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.
KeywordsFisher–Bingham distribution Maximum likelihood estimate Holonomic gradient descent Integrable connection Pfaffian system
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