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

Tomonari Sei, Alfred Kume

Research output: Contribution to journalArticlepeer-review

12 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 languageEnglish
Pages (from-to)321-332
Number of pages12
JournalStatistics and Computing
Volume25
Issue number2
DOIs
Publication statusPublished - 2013 Jan 1

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

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