RUI - New Statistical Methods for Modeling 3-Dimensional Rotations with Advances in the Study of Human Motion

本研究项目致力于发展三维旋转数据的统计方法。当骨骼哺乳动物运动时，它们的骨骼围绕不同的关节旋转，这使得三维旋转的数据在生物力学和人类运动的研究中很常见。虽然研究人员之前的工作在三维方位建模方面取得了进展，但仍有许多类型的统计推断尚未被研究用于旋转数据。该项目通过开发(1)非对称分布类、(2)中值估计器、(3)非参数方法和(4)三维旋转的聚类方法来对人体运动研究中的数据进行建模。产生的新的统计推断技术为生物力学和人体运动研究中的公开问题提供了答案。由于通过本研究项目开发的三维旋转数据的统计推断方法被用于人体运动的研究，它们将为物理治疗中的科学问题提供解决方案。因此，这个项目促进了一所以本科为主的大学数学和理疗系之间的跨学科合作。此外，该项目还包括指导本科生的研究经验，让学生在教育的早期阶段接触到跨学科的研究合作。虽然该项目开发的统计方法主要用于回答人体运动研究中的公开问题，但它也有可能影响出现三维旋转数据的其他领域，如心电向量图和材料科学。

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.