Award Abstract #0239053
CAREER: New Directions in Mixture Models and their Applications

NSF Org:	DMS Division of Mathematical Sciences
Initial Amendment Date:	March 14, 2003
Latest Amendment Date:	May 15, 2006
Award Number:	0239053
Award Instrument:	Continuing grant
Program Manager:	Grace L. Yang DMS Division of Mathematical Sciences MPS Directorate for Mathematical & Physical Sciences
Start Date:	June 1, 2003
Expires:	May 31, 2007 (Estimated)
Awarded Amount to Date:	$313246
Investigator(s):	Ramani Pilla pilla@cwru.edu (Principal Investigator)
Sponsor:	Case Western Reserve University Sears Library, 6th Floor CLEVELAND, OH 44106 216/368-4510
NSF Program(s):	STATISTICS
Field Application(s):	0000099 Other Applications NEC
Program Reference Code(s):	OTHR,9229,1187,1045,0000
Program Element Code(s):	1269

ABSTRACT



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.

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