An empirical Bayes inference for the von Mises distribution

This paper develops an empirical Bayesian analysis for the von Mises distribution, which is the most useful distribution for statistical inference of angular data. A two-stage informative prior is proposed, in which the hyperparameter is obtained from the data in one of the stages. This empirical or approximate Bayes inference is justified on the basis of maximum entropy, and it eliminates the modified Bessel functions. An example with real data and a realistic prior distribution for the regression coefficients is considered via a Metropolis-within-Gibbs algorithm.