A Bayesian model for longitudinal circular data based on the projected normal distribution

The analysis of short longitudinal series of circular data may be problematic and to some extent has not been fully developed. A Bayesian analysis of a new model for such data is presented. The model is based on a radial projection onto the circle of a particular bivariate normal distribution. Inference about the parameters of the model is based on samples from the corresponding joint posterior density, which are obtained using a Metropolis-within-Gibbs scheme after the introduction of suitable latent variables. The procedure is illustrated using both simulated data sets and a real data set previously analyzed in the literature.