Bayesian analysis of circular distributions based on non-negative trigonometric sums

ABSTRACT

Fernández-Durán [Circular distributions based on nonnegative trigonometric sums. Biometrics. 2004;60:499–503] developed a new family of circular distributions based on non-negative trigonometric sums that is suitable for modelling data sets that present skewness and/or multimodality. In this paper, a Bayesian approach to deriving estimates of the unknown parameters of this family of distributions is presented. Because the parameter space is the surface of a hypersphere and the dimension of the hypersphere is an unknown parameter of the distribution, the Bayesian inference must be based on transdimensional Markov Chain Monte Carlo (MCMC) algorithms to obtain samples from the high-dimensional posterior distribution. The MCMC algorithm explores the parameter space by moving along great circles on the surface of the hypersphere. The methodology is illustrated with real and simulated data sets.

KEYWORDS:

• Circular data
• geodesic
• smooth Riemann manifold
• transdimensional Markov Chain Monte Carlo algorithm

AMS SUBJECT CLASSIFICATION:

• 62H11
• 62F15
• 53C22
• 65C60
• 65C05
• 68U20

Acknowledgments

The authors wish to thank the Asociación Mexicana de Cultura A.C. for its support and the reviewers for their useful comments.

Disclosure statement

No potential conflict of interest was reported by the authors.