JTAS Ferreira, MA Juarez and MFJ Steel
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 °exible 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 de¯ned on hyperspheres of any dimension and thus, include the most common circular and spherical cases. Due to the °exibility 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 speci¯cation 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 on the arrival direction of cosmic rays.
Keywords: Directional distributions, hyperspherical splines, mixture of distributions, prior matching, von Mises distributions.