**DEPARTMENT OF COMPUTER SCIENCE
MONASH UNIVERSITY**

**Clayton, Victoria 3168 Australia**

**TECHNICAL REPORT
95/236
**

**
Bayesian estimation of the Von Mises concentration parameter
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*
D L Dowe, J J Oliver, R A Baxter and C S Wallace
*

**ABSTRACT **

The von Mises distribution, M_2(mu, kappa), is a maximum entropy distribution. It corresponds to the distribution of an angle of a compass needle subjected in a uniform magnetic field in direction, mu, with concentration parameter, kappa. The concentration parameter, kappa, is the ratio of the field strength to the temperature of thermal fluctuations.

As such, the von Mises distribution lends itself to a variety of applications.

In earlier work, a Bayesian estimator was obtained for the von Mises distribution parameters using the information-theoretic Minimum Message Length (MML) principle. This MML estimator was shown both to be invariant under twice continuously differentiable 1-1 transformations (such as from polar co-ordinates to Cartesian co-ordinates) and to perform favourably when compared to Maximum Likelihood and a variety of other alternative, non-Bayesian, methods.

In the current work, 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.