Bayesian Model Choice for Directional Data

Abstract

This article is concerned with the problem of choosing between competing models for directional data. In particular, we consider the question of whether or not two independent samples of axial data come from the same Bingham distribution. This is not a straightforward question to answer, due to the intractable nature of the parameter-dependent normalizing constant of the Bingham distribution. We propose three different methods to perform this task within a Bayesian framework, and apply the methodology to a real dataset on earthquakes in New Zealand. R code to run our methods is available in online supplementary materials.