Bayesian tests for circular uniformity

Abstract

Circular data are data measured in angles or directions, which occur in a wide variety of scientific fields. An often investigated hypothesis is that of circular uniformity, or isotropy. Frequentist methods for assessing the circular uniformity null hypothesis exist, but do not allow the user faced with an insignificant result to distinguish lack of power from support for the null hypothesis. Bayesian hypothesis tests, which solve this issue and several others, are developed here. They are easy to compute and perform well, which is shown in a simulation. Two alternative hypotheses are considered. One is based on the von Mises distribution and performs well against unimodal alternatives. Another is based on a kernel density, which acts as an omnibus test against all other scenarios. Assessing the performance of the tests using different priors, it is shown that they are powerful and allow more elaborate conclusions than classical tests of circular uniformity.