LEAPS-MPS: Advancement of Functional Data Inference with Applications to Neuroimaging

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。目前的脑成像技术促进了我们对大脑功能和疾病的理解，如自闭症谱系障碍、帕金森病、创伤性脑损伤和阿尔茨海默病。这项研究将推动这项重要的工作向前发展，以了解大脑疾病是如何与基因变异相互作用的。本研究将为研究单位各级学生提供培训机会，包括数学和统计专业的本科生、硕士生和博士生。培训活动将帮助参与者为继续他们在工业界和学术界的职业生涯做好准备。这项研究还将促进扩大参与，并增加来自代表性不足群体的科学劳动力。此外，这项研究将加强该机构的研究基础设施。该研究旨在开发功能性数据分析工具，以了解动态大脑发育与遗传学和基因组学之间的相互作用。研究者将利用功能数据分类和回归的统计推断方法来识别一些认知障碍的进展。研究的四个具体目标将被调查。第一个目的是研究基于均值和协方差异质性的稳健功能数据分类器的监督投影。第二个目的是研究单个时空曲面的简约半参数重构。第三个目标是研究主题内相关性的正确结合，以便更有效地推断和测试并发功能线性模型。最后一个目标是通过R包实现这些方法，以增强科学和技术的理解。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2). Current brain imaging technologies advance our understanding of brain functionality and disorders such as autism spectrum disorder, Parkinson's disease, traumatic brain injury, and Alzheimer's disease. The research will push this important work forward to understand how a brain disorder develops with possible interaction with genetic variants. The research will provide training opportunities for students from the investigator's institution at all levels, including undergraduate, master, and Ph.D. students in mathematics and statistics. The training activities will help the participants to be prepared to continue their careers in industry and academia. The research will also promote broadening participation and increase the scientific workforce from underrepresented groups. In addition, the research will enhance the research infrastructure at the institution.The research aims to develop functional data analysis tools to understand the interaction between dynamic brain development and genetics and genomics. The investigator will exploit statistical inference methods in functional data classification and regression to identify the progression of some cognitive disorders. Four specific aims of the research will be investigated. The first aim is to study supervised projection based on the heterogeneity in mean and covariance for robust functional data classifiers. The second aim is to investigate parsimonious semiparametric reconstruction of individual spatial-temporal surfaces. The third aim is to study the correct incorporation of within-subject correlation for more efficient inference and testing for concurrent functional linear models. The last aim is to implement the methods through R packages to enhance scientific and technological understanding.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.