Statistical Methodology Commons^™

Flexible Spatial Priors In Bayesian Neuroimaging: Gmrf, Nngp, And Deep Gmrf, Boyoung Hur

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Structural neuroimaging is essential for understanding neurological disorders such as Alzheimer’s disease, enabling accurate delineation of brain regions through image segmentation. Among various segmentation methods, multi-atlas-based approaches like label fusion have become leading techniques. In statistics, Bayesian hierarchical models for label fusion are increasingly favored for their ability to incorporate uncertainty and prior knowledge. Also, a key challenge in modeling neuroimaging data is spatial dependence among image voxels, making the choice of spatial prior critical—particularly in high-resolution settings where segmentation accuracy and computational efficiency are both essential.

This dissertation proposes fully Bayesian spatial hierarchical models that explore two flex- ible …

Experimental Design And Analysis For Decision Making: Methodology And Applications, Yezhuo Li

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This dissertation develops and applies advanced statistical and optimization frameworks to enhance decision-making under uncertainty, particularly in engineering and manufacturing contexts. First, we introduce an approach for the optimal design of controlled experiments that accounts for observational covariates, enabling more precise and personalized decisions. Second, we explore the application of constrained Bayesian optimization, using Gaussian process surrogate models, to optimize composite cure processes, significantly reducing computational effort while maintaining high predictive accuracy. Building on this foundation, we extend Bayesian optimization to bivariate Gaussian process models that capture correlations between objective and constraint functions, offering new insights into multidimensional decision landscapes. …

Selected Topics On Sequential Designs For Decision Making, Caroline Kerfonta

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This dissertation is comprised of three parts. The first proposes a sequential approach to determine the experimental setting with the minimum variance (Kerfonta et al., 2024). Two acquisition functions are developed to assist developing the approach. Theoretical results along with a case study using data from crystallization experiments is conducted to show the ability of the proposed method to correctly select the experiment with the minimum variance. The second and third parts propose adaptations to the Bayesian optimization algorithm using transformed additive Gaussian processes (TAG) as the surrogate model. The goal of using the TAG framework is to decompose the …

A Framework For Statistical Modeling Of Wind Speed And Wind Direction, Eva Murphy

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Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. This dissertation aims to provide a modeling framework for studying the variation of wind speed and wind direction. To this end, three projects are conducted to address some of the key issues for modeling wind vectors.\\

First, a conditional decomposition approach is developed to model the joint distribution of wind speed and direction. Specifically, the …

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

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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 …

Statistical Methods For Modern Threats, Brandon Lumsden

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More than ever before, technology is evolving at a rapid pace across the broad spectrum of biological sciences. As data collection becomes more precise, efficient, and standardized, a demand for appropriate statistical modeling grows as well. Throughout this dissertation, we examine a variety of new age data arising from modern technology of the 21st century. We begin by employing a suite of existing statistical techniques to address research questions surrounding three medical conditions presenting in public health sciences. Here we describe the techniques used, including generalized linear models and longitudinal models, and we summarize the significant associations identified between research …

Advanced High Dimensional Regression Techniques, Yuan Yang

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This dissertation focuses on developing high dimensional regression techniques to analyze large scale data using both Bayesian and frequentist approaches, motivated by data sets from various disciplines, such as public health and genetics. More specifically, Chapters 2 and Chapter 4 take a Bayesian approach to achieve modeling and parameter estimation simultaneously while Chapter 3 takes a frequentist approach. The main aspects of these techniques are that they perform variable selection and parameter estimation simultaneously, while also being easily adaptable to large-scale data. In particular, by embedding a logistic model into traditional spike and slab framework and selecting of proper prior …

Advancements In Gaussian Process Learning For Uncertainty Quantification, John C. Nicholson

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Gaussian processes are among the most useful tools in modeling continuous processes in machine learning and statistics. The research presented provides advancements in uncertainty quantification using Gaussian processes from two distinct perspectives. The first provides a more fundamental means of constructing Gaussian processes which take on arbitrary linear operator constraints in much more general framework than its predecessors, and the other from the perspective of calibration of state-aware parameters in computer models. If the value of a process is known at a finite collection of points, one may use Gaussian processes to construct a surface which interpolates these values to …