Wavelet-based Statistical Modeling and Applications

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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.