Mixture models, which can be viewed also as clustering techniques, have become widely used statistical tools in the analysis of heterogeneous data, aiding researchers in interpreting existing data or in classifying new data. This project extends the current interests of the PI in mixture models to new directions while integrating them into education. It is well known that under the normal mixture model with unequal variance, the likelihood is unbounded and hence the global maximum likelihood estimator (MLE) does not exist. High-dimensional data analysis is becoming increasingly important in many applied fields, including bioinformatics, astronomy and imaging. Moreover, finding the nonparametric MLE is widely regarded as computationally intensive, with the particular difficulty being locating the mass points. To address these issues this project will (1) establish spacings-based inferential tools and asymptotic theory for the normal mixtures with unequal variances to overcome the limitations of the likelihood approach; (2) generalize these methods to multivariate normal mixture model; (3) develop theory and algorithms for multivariate mixtures via the penalized dual method; (4) develop methods for solving nonparametric mixture problems; (5) extend the multivariate mixture methods to identify features in spatial patterns and in turn develop efficient pattern recognition algorithms for use in hyperspectral image classification, mammography and minefield detection; and (6) integrate research and education to advance discovery and understanding of mixtures.
This project will: (1) promote discovery and understanding of the mixture models for modeling univariate and multivariate heterogeneous data; (2) broaden and initiate new applications to advance mixture models to new frontiers; (3) promote collaborative learning and foster critical thinking through student involvement in the PI's research projects; (4) build a firm foundation for the PI in contributing to a well-integrated research and education program in the theory, computation and application of mixture models and related areas; (5) impart education that will train a new generation of scientists and engineers capable of developing mixture models tools to solve important problems arising from new frontiers of biology, engineering and medicine; (6) result in offering an interdisciplinary course in mixture models and applications to graduate students, enabling and promoting interactions between statistics and allied fields; (7) enhance multidisciplinary research experience for students through the PI's collaborations and partnerships with the U.S. Navy and international scientists.
