A new method to simulate the Bingham and related distributions in directional data analysis with applications

TL;DR

This paper introduces an efficient acceptance-rejection method for simulating Bingham distributions on spheres, with potential extensions to related distributions, improving computational approaches in directional data analysis.

Contribution

The paper presents a novel acceptance-rejection algorithm for Bingham distribution simulation using the angular central Gaussian distribution as an envelope, enhancing efficiency and simplicity.

Findings

High efficiency of the proposed method

Straightforward implementation

Potential extensions to Fisher and Fisher-Bingham distributions

Abstract

A new acceptance-rejection method is proposed and investigated for the Bingham distribution on the sphere using the angular central Gaussian distribution as an envelope. It is shown to have high efficiency and to be straightfoward to use. The method can also be extended to Fisher and Fisher-Bingham distributions on spheres and related manifolds.