Bayesian inference for mixtures of von Mises distributions using reversible jump MCMC sampler

Circular data are encountered in a variety of fields. A dataset on music listening behaviour throughout the day motivates development of models for multi-modal circular data where the number of modes is not known a priori. To fit a mixture model with an unknown number of modes, the reversible jump Metropolis-Hastings MCMC algorithm is adapted for circular data and presented. The performance of this sampler is investigated in a simulation study. At small-to-medium sample sizes (Formula presented.), the number of components is uncertain. At larger sample sizes (Formula presented.) the estimation of the number of components is accurate. Application to the music listening data shows interpretable results that correspond with intuition.