Bayesian tests of symmetry for the generalized Von Mises distribution

Bayesian tests on the symmetry of the generalized von Mises model for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007) are introduced. The generalized von Mises distribution is a flexible model that can be axially symmetric or asymmetric, unimodal or bimodal. A characterization of axial symmetry is provided and taken as null hypothesis for one of the proposed Bayesian tests. The Bayesian tests are obtained by the technique of probability perturbation. The prior probability measure is perturbed so to give a positive prior probability to the null hypothesis, which would be null otherwise. This allows for the derivation of simple computational formulae for the Bayes factors. Numerical results reveal that, whenever the simulation scheme of the samples supports the null hypothesis, the null posterior probabilities appear systematically larger than their prior counterpart.