Directional log-spline distributions

Abstract

We introduce a new class of distributions to model directional data, based on hyperspherical log-splines. The class is very flexible and can be used to model data that exhibit features that cannot be accommodated by typical parametric distributions, such as asymmetries and multimodality. The distributions are defined on hyperspheres of any dimension and thus, include the most common circular and spherical cases. Due to the flexibility of hyperspherical log-splines, the distributions can closely approximate observed behaviour and are as smooth as desired. We propose a Bayesian setup for conducting inference with directional log-spline distributions where we pay particular attention to the prior specification and the matching of the priors of the log-splines model and an alternative model constructed through a mixture of von~Mises distributions. We compare both models in the context of three data sets: simulated data on the circle, circular data on the movement of turtles and a spherical application to the arrival direction of cosmic rays.