Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method

Abstract

In this paper we implement the holonomic gradient method to exactly compute the normalising constant of Bingham distributions. This idea is originally applied for general Fisher-Bingham distributions in Nakayama et al. (2011). In this paper we explicitly apply this algorithm to show the exact calculation of the normalising constant; derive explicitly the Pfaffian system for this parametric case; implement the general approach for the maximum likelihood solution search and finally adjust the method for degenerate cases, namely when the parameter values have multiplicities.

References in corpus (4)

• Holonomic Gradient Descent for the Fisher-Bingham Distribution on the $d$-dimensional Sphere
• Holonomic gradient method for the distribution function of the largest root of a Wishart matrix
• The Holonomic Rank of the Fisher-Bingham System of Differential Equations
• Properties and applications of Fisher distribution on the rotation group