Bayesian Circular Statistics: von Mises-based solutions for practical problems

Abstract

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 observed angles, such as wind directions in degrees from north. In that case, the data are best visualized on a circle, and are therefore called . Not just wind directions provide circular data. We run into them 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 bread-and-butter statistician’s toolkit, even something as simple as the mean, can not be used on circular data. Instead, we have to use specialized circular statistics methods. We take a look at several applications, and provide new ways to analyze circular data for practical problems, usually using solutions from the field of . Finally, we’ve created an 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.