This research project focuses on the development of statistical methodology for 3-dimensional rotation data. As skeletal mammals move, their bones rotate around various joints, making data in the form of 3-dimensional rotations common in the study of biomechanics and human motion. While the investigator's previous work has made advances in modeling 3-dimensional orientations, there are many types of statistical inference that have not yet been studied for rotation data. This project models data from the study of human motion by developing (1) a nonsymmetric class of distributions, (2) a median estimator, (3) nonparametric methods, and (4) clustering methods for 3-dimensional rotations. The new statistical inference techniques produced provide answers to open questions in the study of biomechanics and human motion.
As the statistical inference methods for 3-dimensional rotation data developed through this research project are used in the study of human motion, they will lend solutions to scientific problems in physical therapy. Thus, this project promotes interdisciplinary collaboration between the mathematics and physical therapy departments at a predominantly undergraduate university. Additionally, this project includes the mentoring of undergraduate student research experiences, exposing students to interdisciplinary research collaboration at an early stage in their education. While the statistical methodology developed by this project is used primarily to answer open questions in the study of human motion, it has the potential to impact other areas where 3-dimensional rotation data arise, such as vectorcardiography and materials science.
