Bayesian analysis of circular data using wrapped distributions

Circular data arise in a number of different areas such as geological, meteorological, biological and industrial sciences. Standard statistical techniques can not be used to model circular data due to the circular geometry of the sample space. One of the common methods to analyze circular data is known as the wrapping approach. This approach is based on a simple fact that a probability distribution on a circle can be obtained by wrapping a probability distribution defined on the real line. A large class of probability distributions that are flexible to account for different features of circular data can be obtained by the aforementioned approach. However, the likelihood-based inference for wrapped distributions can be very complicated and computationally intensive. The EM algorithm to compute the MLE is feasible, but is computationally unsatisfactory. A data augmentation method using slice sampling is proposed to overcome such computational difficulties. The proposed method turns out to be flexible and computationally efficient to fit a wide class of wrapped distributions. In addition, a new model selection criteria for circular data is developed. Results from an extensive simulation study are presented to validate the performance of the proposed estimation method and the model selection criteria. Application to a real data set is also presented and parameter estimates are compared to those that are available in the literature. © 2011 Copyright Taylor and Francis Group, LLC.