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

Tomonari Sei, Alfred Kume

Research output: Contribution to journalArticle

11 Citations (Scopus)

### 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. (Adv. Appl. Math. 47:639-658, 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.

Original language English 1-12 12 Statistics and Computing https://doi.org/10.1007/s11222-013-9434-0 Accepted/In press - 2013

### Fingerprint

Normalizing Constant
Maximum likelihood
Pfaffian
Maximum Likelihood
Multiplicity

### Keywords

• Bingham distributions
• Directional statistics
• Holonomic functions

### ASJC Scopus subject areas

• Theoretical Computer Science
• Statistics and Probability
• Statistics, Probability and Uncertainty
• Computational Theory and Mathematics

### Cite this

Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method. / Sei, Tomonari; Kume, Alfred.

In: Statistics and Computing, 2013, p. 1-12.

Research output: Contribution to journalArticle

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