Collaborative Research: Analysis of Functional and High-Dimensional Data with Applications

这个项目处理统计推断的现象，导致大量的，多维的和/或功能的数据集。主要的例子是地球物理，生物医学和互联网相关的数据。除了高维性，这些数据通常具有自相似性和非标准（函数）模型的特点，用于建模和统计分析。将要开发的方法将推进函数数据分析的理论和实践，这是一个非常快速发展的现代统计领域。这里提出的统计方法的共同和新颖的特点在于分析数据的性质。多尺度数据表示的最新进展为（i）开发用于估计、测试、分类和反卷积的尺度敏感分析工具以及（ii）描述、总结和建模自相似数据提供了自然和有效的环境。贝叶斯方法将被使用时，eneveravailable先验信息可以被纳入或whenever sensibleautomatic先验是possible.新的推理方法的发展是至关重要的统计支持最近的科学举措和新兴技术。所提出的研究是应用驱动的，因此应用领域的特殊性影响了方法的设计和重点。该提案中提出的技术涉及新医疗方法的有效性测试、目标检测和分类以及医学图像的分类，或更准确地恢复雷达或卫星数据。因此，从该提案中产生的方法适用于卫生、医学和国土安全等战略利益领域。除了方法上的影响，拟议的研究有一个强大的教育组成部分，包括培训研究生，让本科生参与研究项目，举办跨部门研讨会，提高劳动力对职业教育的认识，吸引少数民族和女性学生。

This project deals with statistical inference inphenomena that result in massive, multidimensional and/orfunctional data sets. Prime examples are geophysical, biomedical,and internet related data. In addition to high dimensionality, suchdata are often characterized by self-affinity and requirenon-standard (functional) models for their modeling and subsequentstatistical analysis. The methodology to be developed will advanceboth the theory and practice of functional data analysis, a veryfast-developing and modern area of statistics. The common and novelfeatures of the statistical methods proposed here lie in the natureof analyzed data. The data sets are massive, multidimensional,functional, and possibly self-affine (fractal or multifractal).Recent progress in multiscale data representations provide naturaland efficient environments for (i) developing scale-sensitiveanalyzing tools for estimation, testing, classification, anddeconvolution, and (ii) describing, summarizing, and modelingself-similar data. Bayesian methodology will be used wheneveravailable prior information can be incorporated or whenever sensibleautomatic priors are possible.Development of new inferential methodologies is critical for thestatistical support of recent scientific initiatives and newlyemerging technologies. The proposed research is application driven,so the specificities of the application fields influence the designand focus of the methodology. Techniques suggested in the proposaldeal with problems of testing of efficiency of new medicaltreatments, target detection and classification as well asclassification of medical images, or more accurate recovery of radaror satellite data. Hence, the methodologies which result from theproposal are applicable in such areas of strategic interest ashealth and medicine and homeland security. In addition tomethodological impact, the proposed research has a strongeducational component consisting of training graduate students,involving undergraduate students in research projects, conductinginter-departmental seminars, increasing awareness of mathematicseducation among the work force, and attracting minority and femalestudents.