Level: MSc
Title: Bayesian inference for circular data
Supervisor:

Dr Lawrence Pettit
Research Area: Probability and Applications [Including Statistics]
Description:

Data consisting of angles on a circle can arise in many areas of application. The von Mises distribution is often used to model such data. Both classical and Bayesian methods have been used to make inferences about the parameters of the von Mises distribution. The book by Mardia [6] gives an introduction to this area from a classical viewpoint. Lee [5] gives an introduction to a Bayesian analysis although with a non-informative prior.
Damien and Walker [4] and Nunez-Antonio and Gutierrez-Pena [7] discuss modern computationally intense methods for Bayesian analyses. Collett [3] gives classical methods for detecting outliers in circular data. Tovar and Rivas [8] and Bagchi and Guttman [1] discuss corresponding Bayesian methods. In this project the first aim is to review and explain these methods, concentrating on the Bayesian work. A second aim would be to apply these methods to data simulated from a von Mises distribution (see Best and Fisher [2]).

  1. P. Bagchi and I. Guttman, Spuriosity and outliers in directional data, Journal of Applied Statistics 17 (1990) 341–349.
  2. D.J. Best and N.I. Fisher, Efficient simulation of the von Mises distribution, Applied Statistics 28 (1979) 152–157.
  3. D. Collett, Outliers in circular data, Applied Statistics 29 (1980) 50–57.
  4. P. Damien and S.G. Walker, A full Bayesian analysis of circular data using the von Mises distribution, The Canadian Journal of Statistics 27 (1999) 291–298.
  5. P. Lee, Bayesian Statistics An Introduction. Second edition. Arnold, London, 1997. [Later editions could also be used.]
  6. K.V. Mardia, Statistics of directional data. Academic Press, London, 1972.
  7. G. Nunez-Antonio and E. Gutierrez-Pena, A Bayesian analysis of directional data using the von Mises-Fisher distribution, Communications in Statistics, Simulation and Computation 34 (2005) 989–999.
  8. G.A. Tovar and C.R. Rivas, Outliers in circular data: a Bayesian approach, Qtiesttio 10 (1986) 1–6.
Further Reading:
Key Modules:

MTH6909/MTH709U/MTHM042/MTH776P Bayesian Statistics
Other Information:
Current Availability: Yes