Exact Bayesian Inference for the Bingham Distribution

TL;DR

This paper introduces an exact Bayesian inference method for the Bingham distribution that bypasses the computationally intensive normalising constant, making inference faster and more efficient.

Contribution

It presents a novel approach that avoids calculating the normalising constant, enabling exact Bayesian inference for Bingham distribution parameters.

Findings

Method is simpler to implement

Faster than existing algorithms

Performs better in simulated and real data

Abstract

This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution, which, even when it can be evaluated or accurately approximated, would have to be calculated at each iteration of an MCMC scheme, thereby greatly increasing the computational burden. We propose a method which enables exact (in Monte Carlo sense) Bayesian inference for the unknown parameters of the Bingham distribution by completely avoiding the need to evaluate this constant. We apply the method to simulated and real data, and illustrate that it is simpler to implement, faster, and performs better than an alternative algorithm that has recently been proposed in the literature.