Discordancy Tests for Isotropically Distributed Random Rotations

• Activity Number: 694
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Bryan Stanfill* and Ulrike Genschel
• Companies: CSIRO and Iowa State University
• Keywords: Outlier ; Robust ; Rotation group

Abstract

For data on the real line, circle and even sphere, a plethora of tests are available to identify potentially discordant observations (outliers). When the orientation or rotation of an object in three-dimensions is of interest, however, far fewer tests are available and the existing test generally have low power. In this presentation we propose two test statistics that can be used to test for discordant observations in the rotation group SO(3). The first is a novel statistic that accounts for the topology of the SO(3) space, while the second is an extension of a statistic proposed previously for data on the unit hypersphere. Neither test statistic has a known closed form distribution, therefore we provide two methods to approximate the p-value for the tests. We compare the power of the tests based on each statistic and p-value approximation method in an empirical study. Finally, we demonstrate how our methods can be used to help material scientists correctly identify the composition of metals.