B0617
Title: A skew normal model for consideration on the sphere
Authors: Andriette Bekker - University of Pretoria (South Africa) [presenting]
Delene van Wyk de Ridder - University of Pretoria (South Africa)
JT Ferreira - University of Pretoria (South Africa)
Priyanka Nagar - Stellenbosch University (South Africa)
Abstract: A noteworthy challenge with regard to directional statistics is the fact that many models neglect to address the curvature of underlying sample spaces. To address this problem, the spherical normal distribution was introduced by Hauberg. Borrowing from this approach, and the fact that real-world data are often intrinsically skewed, a spherical skew-normal distribution is proposed for implementation in nonsymmetric learning systems. This density is governed by the squared geodesic distance in the spirit of the intrinsic framework. This implies substituting the standard Euclidean norm with the great-circle distance, which is the length of the shortest path joining two points on the unit sphere. Theoretical results are presented on maximum likelihood estimation and a sampling scheme. An application of model-based clustering is worth investigating within the finite mixture model framework.
