  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.
