Bayesian Inference on the Bimodality of the Generalized von Mises Distribution

Abstract

This article introduces Bayesian inference on the bimodality of the generalized von Mises (GvM) distribution for planar directions (Gatto and Jammalamadaka in Stat Methodol 4(3):341–353, 2007). The GvM distribution is a flexible model that can be axial symmetric or asymmetric, unimodal or bimodal. Two inferential approaches are analysed. The first is the test of null hypothesis of bimodality and Bayes factors are obtained. The second approach provides a two-dimensional highest posterior density (HPD) credible set for two parameters relevant to bimodality. Based on the identification of the two-dimensional parametric region associated with bimodality, the inclusion of the HPD credible set in that region allows us to infer on the bimodality of the underlying GvM distribution. A particular implementation of the Metropolis–Hastings algorithm allows for the computation of the Bayes factors and the HPD credible sets. A Monte Carlo study reveals that, whenever the samples are generated under a bimodal GvM, the Bayes factors and the HPD credible sets do clearly confirm the underlying bimodality.