Bayesian estimation of the von Mises concentration parameter

The von Mises distribution is a maximum entropy distribution. It corresponds to the distribution of an angle of a compass needle in a uniform magnetic field of direction, mu, with concentration parameter, kappa. The concentration parameter, kappa, is the ratio of the field strength to the temperature of thermal fluctuations. Previously, we obtained a Bayesian estimator for the von Mises distribution parameters using the information-theoretic Minimum Message Length (MML) principle. Here, we examine a variety of Bayesian estimation techniques by examining the posterior distribution in both polar and Cartesian co-ordinates. We compare the MML estimator with these fellow Bayesian techniques, and a range of Classical estimators. We find that the Bayesian estimators outperform the Classical estimators.