Wavelet-based Statistical Modeling and Applications

本提案总结了P.I.的当前利益。和未来的方向，在研究和教育。 主题都涉及小波为基础的方法的发展，并代表自然扩展的P.I.以前的工作。三个主要的兴趣领域是：（1）函数数据的贝叶斯聚类。我们的目标是开发新的贝叶斯方法聚类的功能数据。P.I.提出的方法。是基于模型的，并使用无限的混合模型，连同小波系数的选择，描述歧视性的功能的数据。 (2)蛋白质质谱分析。P.I.的总体目标是开发方法提取蛋白质组数据的重要特征，同时结合降维小波技术。私家侦探他对生物信息学领域的兴趣日益浓厚，并与德克萨斯州的许多研究人员建立了合作关系。 (3)基于小波的长记忆数据处理方法。 本项目涉及为时间序列建模开发小波方法。 私家侦探计划建立在她以前的长期记忆估计和变化点检测的工作，并探索新的应用功能性磁共振成像（fMRI）数据。在这个建议中开发的新方法构成了基于小波的方法的理论和实践的进步。从跨学科的合作所产生的数据的应用程序演示了所提出的方法的实用性，并确认小波作为分析数据的工具的成功。所提出的聚类方法是相当普遍的，可以应用到许多不同的上下文，涉及功能数据。私家侦探具有分析近红外光谱研究数据和生物医学数据的经验。她还在生物信息学领域建立了几项合作，并计划开发用于高通量蛋白质质谱分析的小波方法。 这一建议的更广泛影响在于拟议研究的协作性质，也在于其教育和培训目标及其传播成果的努力。私家侦探在得克萨斯州农工大学和其他大学与生命科学研究人员进行了几次合作。她继续从事研究生的指导和培训活动。她还维护一个关于她的研究活动的最新网页，及时张贴论文和附带软件。

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.