Statistical Modeling of Multivariate Functional Data that Exhibit Complex Correlation Structures.

摘要

Due to the large size of modern data sets, there is an ever-increasing need for computationally efficient inferential methods designed for realistic models of large observed functional data sets. The first part of this dissertation introduces an innovative modeling framework for the analysis of multivariate functional data, where each individual functional component exhibits multilevel and spatial structures. The proposed methodology uses a functional principal components based approach for multivariate functional data, which has important advantages in the dimensionality reduction of the data and brings considerable computational savings. Moreover, our approach quantifies the spatial auto- and cross-correlation between units at the lowest level of the hierarchy. The proposed procedure is illustrated through simulation studies and data from a colon carcinogenesis experimental study.;In the second part of the dissertation, we propose a Bayesian modeling framework for jointly analyzing multiple functional responses of different types (e.g. binary and continuous data). Our approach is based on a multivariate latent Gaussian process and models the dependence among the functional responses through the dependence of the latent process. Our framework easily accommodates additional covariates. We offer a way to estimate the multivariate latent covariance, allowing for implementation of multivariate functional principal components analysis to specify basis expansions and simplify computation. We demonstrate our method through both simulation studies and an application to real data from a periodontal study.