New Statistical Modeling Procedures for Object Oriented Data Analysis (OODA)

Colorado State University, Fort Collins CO

Investigators

Abstract

The objectives of this research are to develop novel statistical models, theory, algorithms and applications geared towards the analysis of complex object oriented data, including tree-structured objects and random graphs. The research not only introduces a number of innovative techniques, but also provides various new and deep insights into statistical foundations, e.g., modeling procedure for complex data objects. This research significantly enhances the toolkit available for the analysis of object oriented data. In particular, three inter-related topics are proposed for investigation. First, the investigator develops a careful axiomatic structure for understanding tree-structured objects, which circumvents the need to define linear operations. Moreover, the investigator studies how to carry out statistical inference, based on the metric induced probability measures, in tree space. Nonparametric and semiparametric modeling procedures are also proposed in the space of trees and graphs. Second, a model selection procedure is studied using Hellinger distance. The asymptotic behavior of the estimated Hellinger discrepancy, and testing the adequacy of the approximation are considered. The performance of the proposed model selection procedure is examined through its application to the microarray gene expression data. Third, the investigator develops new techniques for analyzing data collected on manifolds. Manifold data, such as data collected along a river in an ecological study, and data gathered over a surface, have become popular in many scientific fields. New statistical methodology to extract useful features from manifold data is needed. Here, a geodesic low-rank thin plate splines method is under investigation. The research project lays out a well-grounded and comprehensive framework for analysis of object oriented data. It greatly enhances the research on object oriented data analysis by developing interdisciplinary research including bioinformatics, computer science, neuroscience, mathematics and statistics. The research on tree-structured objects can significantly benefit society by developing new techniques in image analysis and improving medical diagnoses. The investigator integrates research and education by working closely with both undergraduate and graduate students, especially underrepresented groups, from various fields. In addition, the results are to be disseminated through presentations, tutorials and conferences and via internet.