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

该奖项全部或部分根据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，以了解大脑疾病如何与遗传变异相互作用。本研究将为研究者所在机构的各级学生提供培训机会，包括本科生、硕士生和博士生。学生在数学和统计。培训活动将帮助参与者做好准备，继续在工业界和学术界的职业生涯。这项研究还将促进扩大参与，增加代表性不足群体的科学工作者。此外，该研究将加强该机构的研究基础设施。该研究旨在开发功能数据分析工具，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。研究者将在功能数据分类和回归中利用统计推断方法来识别某些认知障碍的进展。本研究将探讨四个具体目标。第一个目标是研究基于均值和协方差异质性的监督投影鲁棒函数数据分类器。第二个目标是研究个体时空表面的简约半参数重建。第三个目的是研究如何正确地结合受试者内相关性，以更有效地推断和检验并发功能线性模型。最后一个目标是通过R软件包来实施这些方法，以提高科学和技术的理解。该奖项反映了NSF的法定使命，并被认为值得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来支持。

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.