Inference for circular distributions and processes

One approach to defining models for circular data and processes has been to take a standard Euclidean model and to wrap it around the circle. This generates rich families of circular models but creates difficulties for inference. Using data augmentation ideas which have previously been applied to this problem in the framework of an EM algorithm, we demonstrate the power and flexibility of Markov chain Monte Carlo methods to fit such classes of models to circular data. The precision of the technique is confirmed through simulated examples, and then applications are given to multivariate and time series data of wind directions.