On June 21, 2019, Kees Mulder defended his thesis Bayesian Circular Statistics: von Mises-based solutions for practical problems
Researchers often analyze data that is either numerical, such as height in centimeters, or is divided into categories, such as level of education. However, you can also encounter data like wind directions in degrees. Such data are best visualized on a circle, and are therefore called circular data. We run into this type of data in almost all fields, from psychology to astronomy.
Why is circular data different? Moving one way around the circle means that at some point, we end up back where we started, because 0 = 360. As a result, a lot of the statistician’s toolkit, even something as simple as the mean, can not be used on circular data.
We take a look at several applications, and provide new ways to analyze circular data for practical problems, usually using solutions from Bayesian statistics.
For example, in cognitive psychology of haptic behavior there are experiments with a circular outcome. To relate both numerical and categorical predictors to the circular outcome, we made a new circular regression model, which uses the predictors in a better way than earlier models. Other problems we worked on are testing whether directions are spread evenly on the circle, analysis of the times at which people listened to certain music genres, models for eye movement directions obtained in eye tracking research, and modeling crime times in criminology.
Finally, we’ve created an R package, circbayes, that can perform these analyses in a user-friendly way. As a result, the field of Bayesian circular statistics has both been expanded in the scope of its analyses, as well as the accessibility of its methods.
Prof. Dr. Herbert Hoijtink & Dr. Irene Klugkist