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

2013/04/30 by Tomonari Sei, Sei, Tomonari, Alfred Kume +1
Computer Science · Mathematics · #Advanced Statistical Methods and Models #Bayesian Methods and Mixture Models #Computation (stat.CO) #FOS: Computer and information sciences #Morphological variations and asymmetry

paper · pdf · doi:10.48550/arxiv.1304.7973

openalex publication_date 2013/04/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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