This article introduces two new Bayesian nonparametric models for circular data based on Dirichlet process (DP) mixtures of normal distributions. The first model is a projected DP mixture of bivariate normals and the second approach is based on a wrapped DP mixture of normal distributions. We show how to carry out inference for these models based on a slice sampling scheme and introduce an approach to estimating a variant of the deviance information criterion which is appropriate in the context of latent variable models. Our models are then compared with both simulated and real data examples.
circular data; deviance information criterion; dirichlet process mixtures; projected normal distribution; wrapped normal distribution