MML Estimation of the Parameters of the Sherical Fisher Distribution

Abstract

The information-theoretic Minimum Message Length (MML) principle leads to a general invariant Bayesian technique for point estimation. We apply MML to the problem of estimating the concentration parameter, κ , of spherical Fisher distributions. (Assuming a uniform prior on the field direction, μ , MML simply returns the Maximum Likelihood estimate for μ. ) In earlier work, we dealt with the von Mises circular case, d =2. We say something about the general case for arbitrary d ≥ 2 and how to derive the MML estimator, but here we only carry out a complete calculation for the spherical distribution, with d =3. Our simulation results show that the MML estimator compares very favourably against the classical methods of Maximum Likelihood and marginal Maximum Likelihood (R.A. Fisher (1953), Schou (1978)). Our simulation results also show that the MML estimator compares quite favourably against alternative Bayesian methods.