Wavelet-based Statistical Modeling and Applications

这份提案总结了私人投资机构目前在研究和教育方面的兴趣和未来的发展方向。所有主题都涉及到基于小波方法的发展，并代表了P.I.S以前工作的自然延伸。感兴趣的三个主要领域是：(1)函数数据的贝叶斯聚类。其目的是开发新的贝叶斯方法用于功能数据的聚类。P.I.提出的方法是基于模型的，使用无限混合模型和描述数据区别性特征的小波系数的选择。(2)蛋白质质谱分析。P.I.的总体目标是开发提取蛋白质组数据重要特征的方法，同时结合降维小波技术。P.I.对生物信息学领域的兴趣与日俱增，并与德克萨斯A&M公司的许多调查人员建立了合作关系。(3)基于小波的长记忆数据方法。该项目涉及用于时间序列建模的小波方法的发展。这位P.I.计划在她之前在长记忆估计和变点检测方面的工作的基础上，探索功能磁共振成像(FMRI)数据的新应用。本提案中提出的新方法是基于小波方法的理论和实践的进步。对跨学科合作产生的数据的应用表明了所建议方法的实际用处，并证实了小波作为分析数据的工具的成功。所提出的聚类方法是非常通用的，并且可以应用于涉及功能数据的许多不同的上下文。P.I.以前有过分析涉及近红外光谱和生物医学数据的研究数据的经验。她还在生物信息学领域建立了几个合作伙伴，并计划开发用于高通量蛋白质质谱分析的小波方法。这项建议的更广泛影响不仅体现在拟议研究的协作性质，而且还体现在其教育和培训目标以及传播成果的努力方面。在德克萨斯农工大学和其他大学，P.I.与生命科学领域的研究人员进行了几次合作。她继续参与研究生的辅导和培训活动。她还维护一个关于她的研究活动的最新网页，及时在那里张贴论文和附带的软件。

This proposal summarizes current interests of the P.I. and future directions, in both research and education. Topics all involve the development of wavelet-based methods and represent natural extensions of the P.I.'s previous work. The three main areas of interest are: (1) Bayesian Clustering of Functional Data. The objective is to develop novel Bayesian methods for clustering of functional data. The approach proposed by the P.I. is model-based and uses infinite mixture models together with the selection of wavelet coefficients describing discriminatory features of the data. (2) Analysis of Protein Mass Spectra. The overall goal of the P.I. is to develop methodologies for extracting important features of proteomic data whileincorporating dimension reduction wavelet techniques. The P.I. has a growing interest in the area of Bioinformatics and has established collaborations with a number of investigators at Texas A&M. (3) Wavelet-based Methods for Long Memory Data. This project relates to the development of wavelet methods for time series modelling. The P.I. plans to build on her previous work on long memory estimation and on change-point detection and to explore novel applications to functional Magnetic Resonance Imaging (fMRI) data. The novel methodologies developed in this proposal constitute advances in the theory and practice of wavelet-based methods. Applications to data arising from interdisciplinary collaborations demostrate the practical usefulness of the proposed methods, and confirm the success of wavelets as a tool for analysing data. The proposed clustering methods are quite general and can be applied to a number of different contexts that involve functional data. The P.I. has previous experience with the analysis of data from studies involving Near Infrared spectra and of biomedical data. She has also established several collaborations in the area of Bioinformatics and plans to develop wavelet methods for the analysis of high-throughput protein mass spectra. Broader impacts of this proposal are in the collaborative nature of the proposed research but also in its educational and training objectives and in its efforts to disseminate results. The P.I. is engaged in several collaborations with investigators in the life sciences, both at Texas A&M and at other universities. She continues her engagement in the mentoring of graduate students and in training activities. She also maintains an updated webpage on her research activities where papers and accompanying software are posted in a timely manner.