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

Sei, Tomonari, Kume, Alfred (2015) Calculating the normalising constant of the Bingham distribution on the sphere using the holonomic gradient method. Statistics and Computing, 25 (2). pp. 321-332. ISSN 0960-3174. E-ISSN 1573-1375. (doi:10.1007/s11222-013-9434-0) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:54546)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
Official URL: http://doi.org/10.1007/s11222-013-9434-0

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.

Item Type:	Article
DOI/Identification number:	10.1007/s11222-013-9434-0
Uncontrolled keywords:	Bingham distributions, Directional statistics, Holonomic functions
Subjects:	Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Divisions:	Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User:	Alfred Kume
Date Deposited:	15 Mar 2016 21:55 UTC
Last Modified:	05 Nov 2024 10:42 UTC
Resource URI:	https://kar.kent.ac.uk/id/eprint/54546 (The current URI for this page, for reference purposes)

University of Kent Author Information

Kume, Alfred.

Creator's ORCID:	https://orcid.org/0000-0001-7683-1693
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