Gyuhyeong Goh (University of Connecticut): Bayesian Model Selection for Circular Data with Wrapped Distribution

A wrapping approach has played a major role to analyze circular data, which arise in various scientific fields, especially in biology. While a rich class of distributions for circular data can be generated by the wrapping approach, it leads infinite summations in a given wrapped density function. As a result, the inference procedure for the wrapped distribution becomes complicated. To overcome the challenge, Ravindran and Ghosh (2012) introduced a practical Bayesian method to estimate parameters in a wide class of wrapped distributions. In contrast to the parameter estimation, there is a few literature in a model selection procedure for Bayesian modeling with the wrapped distributions. In this paper, we propose a new Bayesian model selection criterion for the wrapped distributions along with its Monte Carlo estimator. The proposed criterion, named Bregman Divergence Criterion, generalizes and unifies varied Bayesian model selection methods including Bayes factor, pseudo-Bayes factor, and Intrinsic Bayes factor. To check the statistical consistency associated with our model selection method, a practical implementation of the calibration method based on a probability integral transform is introduced via a Monte Carlo method. The methodology is exemplified via simulation studies and real data analysis.

Joint work with Dipak K. De