Statistical Methods for Spatially Correlated Hierarchical Functional Data

North Carolina State University, Raleigh NC

Investigators

Abstract

This research project is to create new statistical models and methods for the analysis of hierarchical functional data. In particular the investigator proposes a novel methodological framework for fast and robust inferential tools when the true data generating process accounts for complex correlation mechanisms that mimic and represent true biological structures. The project has the following aims. (a). To develop a new methodological framework for the analysis of hierarchical univariate functional data when the functions at the lowest level of hierarchy are correlated. Understanding and quantifying the dependence structure between these functions is of scientific importance. (b). To extend the developed methodology to the analysis of multivariate functional data. (c). To propose new inferential methods for group means and differences between group means when functional data have a natural hierarchical and spatial structure. Modern research data have become increasingly complex, raising non-traditional modeling and inferential challenges. In particular, advancements in technology and computation have made recording and processing of functional data possible. An increasing number of scientific experiments record hierarchical functional data with complex dependence structures. Although the proposed research was motivated by data from a colon cancer experimental study, correlated functional data arise in many areas of research. The statistical methods developed in this proposal are timely and important and will be relevant to many new data sets, where the object of inference are functions or images that remain dependent even after conditioning on the subject on which they are measured. Such data are collected in engineering and climate modeling among others. In contrast with other published methods, the methodology proposed here is computationally efficient and it scales well to moderate and large data sets.