A Semiparametric Bayesian Model for Circular-Linear Regression

Abstract

Circular data are observations that are represented as points on a unit circle. Times of day and directions of wind are two such examples. In this work, we present a Bayesian approach to regress a circular variable on a linear predictor. The regression coefficients are assumed to have a nonparametric distribution with a Dirichlet process prior. The semiparametric Bayesian approach gives added flexibility to the model and is useful especially when the likelihood surface is ill behaved. Markov chain Monte Carlo techniques are used to fit the proposed model and to generate predictions. The method is illustrated using an environmental data set.

Keywords:

• Directional data
• Dirichlet process
• MCMC
• Predictive density
• von Mises distribution

Mathematics Subject Classification:

• 62G08

Acknowledgments

We extend our thanks to the referee for comments that led to a considerable improvement of this article. We also thank Dr. Peter Finkelstein of the Atmospheric Modeling Division, U.S. Environmental Protection Agency, for providing the data used in the illustration and for consulting on their use, and we thank Dr. Brian Eder, also of the Atmospheric Modeling Division, for comments on the synoptic scale.