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

该奖项的全部或部分资金来自《2021年美国救援计划法案》(公法117-2)。目前的脑成像技术促进了我们对大脑功能和疾病的了解，如自闭症谱系障碍、帕金森氏症、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推进，以了解大脑障碍是如何发展的，并可能与基因变异相互作用。这项研究将为各级研究机构的学生提供培训机会，包括本科生、硕士和博士生在数学和统计方面的培训。培训活动将帮助学员为在工业界和学术界继续他们的职业生涯做好准备。这项研究还将促进更广泛的参与，并增加代表不足的群体的科学劳动力。此外，这项研究还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。研究人员将利用功能数据分类和回归中的统计推断方法来确定一些认知障碍的进展。这项研究的四个具体目标将被调查。第一个目标是研究基于均值和协方差异质性的监督投影在稳健函数数据分类器中的应用。第二个目标是研究单个时空曲面的简约半参数重建。第三个目标是研究如何正确地结合被试内部相关性，以便对并发函数线性模型进行更有效的推理和测试。最后一个目标是通过R包实施这些方法，以增进对科学和技术的理解。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.