Statistical Models Commons^™

Learning Graphical Models Of Multivariate Functional Data With Applications To Neuroimaging, Jiajing Niu

All Dissertations

This dissertation investigates the functional graphical models that infer the functional connectivity based on neuroimaging data, which is noisy, high dimensional and has limited samples. The dissertation provides two recipes to infer the functional graphical model: 1) a fully Bayesian framework 2) an end-to-end deep model.

We first propose a fully Bayesian regularization scheme to estimate functional graphical models. We consider a direct Bayesian analog of the functional graphical lasso proposed by Qiao et al. (2019).. We then propose a regularization strategy via the graphical horseshoe. We compare both Bayesian approaches to the frequentist functional graphical lasso, and compare the …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Online Variational Bayes Inference For High-Dimensional Correlated Data, Sylvie T. Kabisa, Jeffrey S. Morris, David Dunson

Jeffrey S. Morris

High-dimensional data with hundreds of thousands of observations are becoming commonplace in many disciplines. The analysis of such data poses many computational challenges, especially when the observations are correlated over time and/or across space. In this paper we propose exible hierarchical regression models for analyzing such data that accommodate serial and/or spatial correlation. We address the computational challenges involved in fitting these models by adopting an approximate inference framework. We develop an online variational Bayes algorithm that works by incrementally reading the data into memory one portion at a time. The performance of the method is assessed through simulation studies. …

Functional Car Models For Spatially Correlated Functional Datasets, Lin Zhang, Veerabhadran Baladandayuthapani, Hongxiao Zhu, Keith A. Baggerly, Tadeusz Majewski, Bogdan Czerniak, Jeffrey S. Morris

Jeffrey S. Morris

We develop a functional conditional autoregressive (CAR) model for spatially correlated data for which functions are collected on areal units of a lattice. Our model performs functional response regression while accounting for spatial correlations with potentially nonseparable and nonstationary covariance structure, in both the space and functional domains. We show theoretically that our construction leads to a CAR model at each functional location, with spatial covariance parameters varying and borrowing strength across the functional domain. Using basis transformation strategies, the nonseparable spatial-functional model is computationally scalable to enormous functional datasets, generalizable to different basis functions, and can be used on …

Bayesian Function-On-Function Regression For Multi-Level Functional Data, Mark J. Meyer, Brent A. Coull, Francesco Versace, Paul Cinciripini, Jeffrey S. Morris

Jeffrey S. Morris

Medical and public health research increasingly involves the collection of more and more complex and high dimensional data. In particular, functional data|where the unit of observation is a curve or set of curves that are finely sampled over a grid -- is frequently obtained. Moreover, researchers often sample multiple curves per person resulting in repeated functional measures. A common question is how to analyze the relationship between two functional variables. We propose a general function-on-function regression model for repeatedly sampled functional data, presenting a simple model as well as a more extensive mixed model framework, along with multiple functional posterior …

Functional Regression, Jeffrey S. Morris

Jeffrey S. Morris

Functional data analysis (FDA) involves the analysis of data whose ideal units of observation are functions defined on some continuous domain, and the observed data consist of a sample of functions taken from some population, sampled on a discrete grid. Ramsay and Silverman's 1997 textbook sparked the development of this field, which has accelerated in the past 10 years to become one of the fastest growing areas of statistics, fueled by the growing number of applications yielding this type of data. One unique characteristic of FDA is the need to combine information both across and within functions, which Ramsay and …

Ordinal Probit Wavelet-Based Functional Models For Eqtl Analysis, Mark J. Meyer, Jeffrey S. Morris, Craig P. Hersh, Jarret D. Morrow, Christoph Lange, Brent A. Coull

Jeffrey S. Morris

Current methods for conducting expression Quantitative Trait Loci (eQTL) analysis are limited in scope to a pairwise association testing between a single nucleotide polymorphism (SNPs) and expression probe set in a region around a gene of interest, thus ignoring the inherent between-SNP correlation. To determine association, p-values are then typically adjusted using Plug-in False Discovery Rate. As many SNPs are interrogated in the region and multiple probe-sets taken, the current approach requires the fitting of a large number of models. We propose to remedy this by introducing a flexible function-on-scalar regression that models the genome as a functional outcome. The …

Statistical Methods For Proteomic Biomarker Discovery Based On Feature Extraction Or Functional Modeling Approaches, Jeffrey S. Morris

Jeffrey S. Morris

In recent years, developments in molecular biotechnology have led to the increased promise of detecting and validating biomarkers, or molecular markers that relate to various biological or medical outcomes. Proteomics, the direct study of proteins in biological samples, plays an important role in the biomarker discovery process. These technologies produce complex, high dimensional functional and image data that present many analytical challenges that must be addressed properly for effective comparative proteomics studies that can yield potential biomarkers. Specific challenges include experimental design, preprocessing, feature extraction, and statistical analysis accounting for the inherent multiple testing issues. This paper reviews various computational …

Wavelet-Based Functional Linear Mixed Models: An Application To Measurement Error–Corrected Distributed Lag Models, Elizabeth J. Malloy, Jeffrey S. Morris, Sara D. Adar, Helen Suh, Diane R. Gold, Brent A. Coull

Jeffrey S. Morris

Frequently, exposure data are measured over time on a grid of discrete values that collectively define a functional observation. In many applications, researchers are interested in using these measurements as covariates to predict a scalar response in a regression setting, with interest focusing on the most biologically relevant time window of exposure. One example is in panel studies of the health effects of particulate matter (PM), where particle levels are measured over time. In such studies, there are many more values of the functional data than observations in the data set so that regularization of the corresponding functional regression coefficient …

Bayesian Random Segmentationmodels To Identify Shared Copy Number Aberrations For Array Cgh Data, Veerabhadran Baladandayuthapani, Yuan Ji, Rajesh Talluri, Luis E. Nieto-Barajas, Jeffrey S. Morris

Jeffrey S. Morris

Array-based comparative genomic hybridization (aCGH) is a high-resolution high-throughput technique for studying the genetic basis of cancer. The resulting data consists of log fluorescence ratios as a function of the genomic DNA location and provides a cytogenetic representation of the relative DNA copy number variation. Analysis of such data typically involves estimation of the underlying copy number state at each location and segmenting regions of DNA with similar copy number states. Most current methods proceed by modeling a single sample/array at a time, and thus fail to borrow strength across multiple samples to infer shared regions of copy number aberrations. …