Statistics and Probability Commons^™

Who Am I As A Learner? The Effects Of A Self-Regulated Learning Intervention On Ninth Graders’ Academic Self-Concepts And Intrinsic Motivation, Kaitlyn Elizabeth Bailey

Theses and Dissertations

The transition from middle school to high school is a notoriously difficult one, and a student’s success in ninth grade is typically a predictor of future success in high school. Unfortunately, many ninth graders struggle to engage in school. Despite their capability to complete the work, these students appear unmotivated and simply disengaged from school. In this action research case study, three students had the opportunity to share their education stories and the experiences that have shaped their academic self-concepts. These students also participated in a self-regulated learning intervention to determine if students’ feelings of autonomy, competence, and relatedness could …

Bayesian Joint Modeling Of Longitudinal Data And Interval-Censored Failure Time Data, Yuchen Mao

Theses and Dissertations

Longitudinal data are a collection of repeated observations of the same subjects at different points in time. Interval-censored data arise when the time to the event of interest for each subject is never exactly observed but known to fall between two consecutive points in time. Joint analysis of longitudinal data and interval-censored failure time data can lead to more accurate estimates compared to separate modeling when the correlation among events of interest or intracluster correlation is present. The aim of this dissertation is to develop efficient and reliable joint analyses of longitudinal and interval-censored failure time data using Bayesian methods. …

Beyond Homogeneity: Exploring Causal Heterogeneity In Psychopathology, Philip B. Vinh

Theses and Dissertations

Traditional models in psychiatric research often impose assumptions of causal homogeneity, treating population-level associations as reflective of uniform underlying mechanisms. This dissertation challenges that assumption by introducing statistical and machine learning frameworks designed to detect and model causal heterogeneity in the development of psychopathology. Central to this approach is the advancement of finite mixture structural equation modeling (FM-SEM) to identify latent subgroups characterized by distinct, and sometimes opposing, causal pathways.

The dissertation comprises three integrated empirical studies. The first introduces mixDoC, a finite mixture extension of the classical Direction of Causation (DoC) model applied to twin data, enabling the detection …

Predictive Inference For Ion Concentration With Machine Learning And Bayesian Methods, Alexandra B. Ulbing

Theses and Dissertations

Ultraviolet--visible (UV--Vis) spectroscopy produces high-dimensional signals that are strongly collinear, shift with concentration, and exhibit heteroskedastic, non-Gaussian noise. These features make supervised regression from spectra to ionic concentrations statistically challenging and limit the reliability of methods that assume linear structure or homoscedastic errors.

This dissertation develops two complementary frameworks for prediction and uncertainty quantification in UV--Vis spectroscopic regression: (1) frequentist stacked ensembles combined with distribution-free conformal prediction, and (2) Bayesian hierarchical modeling and Bayesian stacking. Together, they provide a unified view of model-based and distribution-free uncertainty across nickel and nickel--cobalt datasets.

The frequentist component builds ensembles of Functional Data Analysis …

Analyzing Factors Influencing Employee Turnover In Tech Companies: A Predictive Modeling Approach, Shinjon Ghosh

Theses and Dissertations

Employee turnover poses substantial challenges for technology firms, and understanding its key drivers through predictive modeling is essential for developing effective retention strategies. This study investigates factors influencing employee turnover in technology companies by implementing a predictive modeling approach on the IBM HR Analytics Employee Attrition dataset. The research aims were identifying key factors contributing to employee attrition, developing predictive models to forecast turnover risk, and analyzing interactions among significant predictors. By examining a range of features, the results highlight significant variables (Over Time, Monthly Income, Marital Status, etc.) of attrition and offer actionable insights for developing targeted employee retention …

Optimal Data Splitting Methods, Sujay Mudalgi

Theses and Dissertations

In predictive modeling, effective data splitting is crucial for creating statistically representative training and validation sets. The state-of-the-art data splitting methods are based on minimizing the energy distance between the split subsets. However, there are a number of limitations in the existing methods, which this dissertation aims to address. First, the existing methods were computationally inefficient. Thus, Chapter 2 proposes a method to scale up these approaches for big data. Here, we introduce scalable Twinning (s-Twinning), which significantly improves the execution speed of data splitting without sacrificing accuracy. Second, the existing methods did not consider the predictive relationship in the …

Machine Learning Models Leveraging Patient-Similarity And Clinical Temporality For Disease Prognoses, Ahmad F. Al Musawi

Theses and Dissertations

Electronic Health Records (EHRs) constitute a comprehensive and high-dimensional repository of clinical data, encompassing a wide array of patient-level information such as diagnoses, procedures, medications, laboratory results, and unstructured clinical narratives. These data hold immense potential for advancing predictive modeling in healthcare, including tasks such as disease progression modeling, hospital readmission prediction, and length of stay (LoS) estimation. However, the intrinsic complexity of EHR data—manifested in its heterogeneity, sparsity, and temporal dynamics—poses significant analytical challenges that limit the generalizability and interpretability of conventional machine learning models. Recent methodological advancements in deep learning and graph-based learning, particularly Graph Neural Networks (GNNs), …

An Adaptive Method For Covariate Balancing In Block Randomized Clinical Trials, Ren Rasnick

Theses and Dissertations

Clinical trials are randomized in part to limit allocation bias, but also to ensure comparability between treatment arms for a baseline variable of concern. Comparable with regard to a baseline variable of concern is necessary for the validity of statistical methods. However, comparability is not guaranteed for trials of any size and is even more likely in trials with < 200 total participants. We propose a new method for adapting the allocation of participants in a sequentially allocated two-armed study with a small sample size to better ensure comparability.

The proposed method calculates the expected final imbalance (lack of comparability) based on the current participant values. Unlike several other methods, our method ensures the final desired sample size for each treatment arm, utilizes the expected final imbalance, increases comparability between …

Predictive Modeling For Healthcare Data Using Nonlinear Bayesian Methods, Prince Kofi Asare

Theses and Dissertations

Unplanned hospital readmissions represent a significant challenge for healthcare systems, contributing to substantial financial burdens and highlighting gaps in patient care coordination. In the U.S., approximately 20% of Medicare beneficiaries are readmitted within 30 days, costing billions annually. Social determinants of health, such as income, housing stability, and social support, account for up to 80% of health outcomes, yet their integration into predictive models remains underexplored. This study introduces a novel Bayesian framework for predicting 30-day readmission risk, combining Gaussian Process models with spike-and-slab priors and Bayesian Lasso regression with Laplace priors. Utilizing Markov Chain Monte Carlo methods, the approach …

Method For Measuring The Rate Of Improvement In Survival Times Of Cancer Patients, Thobani Chaduka

Theses and Dissertations

In clinical settings, technological advancements have facilitated health care improvements in data analytics, artificial intelligence, telemedicine, health information systems, etc. This has furthered our understanding of cancer biology and treatment mechanisms. In this study, we aim to understand whether Moore’s law-like models may derive from historical cancer survival data, and how they can predict survival statistics for newly diagnosed cancer patients. Historically these predictions have previously been done with the diagnosis year as the independent variable and the survival as a dependent variable. In this study we use death year data as an independent variable and from that, we derive …

Bayesian Lasso Regularized Quantile Regression And Its Applications, Priscilla Kissi-Appiah

Theses and Dissertations

Since the pioneering work of (Koenker and Bassett Jr 1978), quantile regression has been a popular regression technique that helps researchers investigate a whole distribution of the response variable. In addition, due to the quantile check loss function, it is robust against outliers and heavy-tailed distributions of the response variable and can provide a more comprehensive picture of modeling via exploring the conditional quantiles of the response variable. In this research, we study the lasso regularized quantile regression from a Bayesian perspective. We develop an efficient sampling algorithm to generate posterior samplings for making posterior inference by using a location-scale …

Decoding Neural Networks: An Information-Theoretic Guide To Interpretability, Error Analysis And Efficiency, Mackenzie J. Meni

Theses and Dissertations

This dissertation addresses critical challenges in neural network design by leveraging entropy-based techniques to improve model efficiency, interpretability, and bias reduction. Focusing on the unique demands of computer vision applications, particularly object detection and classification for real-time systems, this work introduces a series of innovative methods centered on information theory. At the core of these methods is the Probabilistic Explanations of Entropic Knowledge (PEEK) framework, a tool developed to analyze and visualize entropy distributions across feature maps. PEEK offers insights into information flow within neural networks, making it possible to pinpoint layers that contribute meaningfully to decision-making or identify those …

Bayesian Nonparametric Models For Pooled Data, Yizeng Li

Theses and Dissertations

This work examines two applications of pooling: group testing and pooled biomonitoring. Group testing, introduced by Dorfman in the early 1940s, was initially developed to screen for syphilis among U.S. inductees during World War II. Since then, the approach has demonstrated cost-saving benefits in diverse fields, including drug discovery, genetics, and infectious disease testing. While various regression methods—parametric, nonparametric, and semiparametric—have been proposed to analyze group testing data, they fall short in addressing age-related disparities in disease presence if such variations exist. In Chapter 2, we address this gap by expanding varying coefficient regression within a Bayesian framework to accommodate …

Bayesian Methods In Analyzing The Diagnostic Accuracy\\ For Ordinal Ratings, Yun Yang

Theses and Dissertations

This dissertation focuses on ordinal classification ratings, which are commonly used in medical practice to assess the severity of a disease or condition. For example, a group of radiologists rate a set of mammograms and assign BI-RADS (Breast Imaging Reporting Data System) score for each mammogram. A Bayesian probit hierarchical model is first proposed to analyze this type of data. It links the ordinal ratings with both rater diagnostic skills and patient latent disease severity. Each rater diagnostic skills are quantified with two parameters, diagnostic bias and diagnostic magnifier. Patient latent disease severity is assumed to follow a different normal …

Simulation Study On Count Data Based On Double Poisson Distribution, Chao Ma

Theses and Dissertations

This thesis delves into the double Poisson distribution. Regression based on the double Poisson distribution, as proposed by Efron in 1986, offers an alternative approach that allows for more accurate regression models when dealing with discrete data that exhibit either over- or under-dispersion compared to the Poisson distribution. In this thesis, two methods of calculating the exact double Poisson density are compared: one utilizes the exact probability with the normalizing constant c(mu, theta) by definition or the “finite sum” method, while the other employs an approximation of the normalizing constant c(mu, theta). Furthermore, a simulation was …

Statistical Inference Based On Elliptically Symmetric Distributions For Directional Data, Zehao Yu

Theses and Dissertations

Directional data arise in many scientific fields such as meteorology, oceanography, geology, zoology, and biomechanics. Geometrically, directional data lie in a spherical space. Although not in a spherical space, compositional data, such as microbiome data, can be mapped from a simplex to a spherical space via the component-wise square-root transformation. Other examples where compositional data emerge as a subject of interest include compositions of minerals in rocks, compositions of chemical mixtures, investment portfolios, and demographic composition of a population. This dissertation aims to develop inference procedures for analyzing directional data in general initially, with later focus shifted to the transformed …

Evaluating The Influence Of Perfluorooctane Sulfonic Acid Exposure On Blood Glucose Levels: A Comprehensive Multiple Regression Analysis Considering Confounding Factors, Henry Mensah

Theses and Dissertations

Perfluorooctane sulfonate (PFOS) are widely used for industrial and commercial purposes and have received increasing attention due to their adverse effects on health. This thesis investigates the relationship between PFOS exposure and blood glucose levels, considering potential confounding factors. Regression analysis was conducted on a dataset comprising demographic, lifestyle, and biomarker data from a diverse population sample. Sex exhibited a significant role, with females demonstrating an 11.77% increase in blood glucose levels in response to PFOS exposure compared to males, supported by a p-value of 1.04 × 109. Body mass index (BMI) also played a pivotal role, revealing a 2.17% …

A Spatial Decision Support System For Rent Estimation Of Retail Spaces In Manhattan Using Geographically Weighted Regression And Spatial Regression, Andie M. Migden Miller

Theses and Dissertations

This report outlines an automated, three-phase Spatial Decision Support System that creates models to estimate rent of retail spaces across Manhattan. First, enrich data with predictors. Second, optimize spatially aware neighborhood-level models by combining GWR, spatial regression, and non-spatial regression. Finally, visualize results in an Esri-based WebApp.

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Forecasting Stock Prices Using Arima Models And Technical Analysis, Muath I. Almaiman

Theses and Dissertations

This thesis explores the integration of Autoregressive Integrated Moving Average (ARIMA) models and technical analysis to forecast stock prices, with a focus on Coca-Cola's (KO) and Netflix’s (NFLX) stocks. It examines the effectiveness of combining ARIMA models, known for their predictive accuracy in time-series analysis, with technical indicators, particularly moving averages. The study evaluates whether this integrated approach can enhance the predictive capability of stocks prices beyond traditional methods. The predictive capability is evaluated using error metrics from the ARIMA models, as well as by assessing the return earned using simple rules based on the technical indicators. Utilizing data spanning …

An Analysis Of China’S Perceived Geographic Locations Of Interest By Use Of Value Informed Facility Location Models, Layton C. Hedge

Theses and Dissertations

This research examines China and derives insights specific to it and the First Island Chain and the Second Island Chain. In doing so, this research demonstrates a methodology to examine other competitors and their geostrategic interests. In the first phase of analysis, it develops a value hierarchy to depict objectives within subregions of the area of interest and considers four alternative weightings of the value hierarchy. In the second phase of analysis, it applies four location-covering models to assess how the competitor would emplace a range of limited resources to deter and/or control points of interest. Results indicate that land-based …

Examining The Effect Of Contractor Logistics Support On The Reliability Of Military Aircraft, Rodrigo S. Campos De Moura

Theses and Dissertations

This study utilizes survival analysis for examining the effect of Contractor Logistics Support (CLS) on the reliability of military aircraft before and after implementing CLS. The provider of CLS in this study is the original equipment manufacturer that designed and produced the target aircraft of this study, the Embraer A-29 Super Tucano.

Simulating Human-Autonomous Aircraft Teams In An Anti-Access Area Denial (A2ad) Environment, Michael Kaminski

Theses and Dissertations

The role of autonomy has evolved recently, demanding tighter integration between human and autonomous systems, particularly in highly contested A2AD environments. Near-peer adversaries have modernized their integrated air defense systems (IADS), diminishing the current advantages of the United States Air Force. To regain air dominance, efforts like the Collaborative Combat Aircraft (CCA) program are underway, aiming to deploy unmanned autonomous alongside manned next-generation fighter aircraft. This research assesses various operational concepts, focusing on autonomous tactics post-manned fighter loss, strike timing of independent teams, and weapon configuration observability. Using the Advanced Framework for Simulation, Integration and Modeling (AFSIM), an agent-based model …

Housing Preferences And Vertical Expansion Potential In Riyadh City, Nasser R. Alrashed

Theses and Dissertations

This research investigates the demand for apartment living in Riyadh's northern area and assesses its implications for vertical urban development, aligning with Saudi Arabia's Vision 2030. Employing a quantitative methodology, a structured survey was distributed to a diverse cross-section of Riyadh's population, focusing on housing preferences and perceptions of vertical living. Key findings indicate a significant demand for apartments, primarily from young to middle-aged, smaller households in low to middle-income brackets. Notably, a substantial portion of respondents showed a preference for high-rise living, suggesting a readiness for vertical expansion to manage the city's growing population. The study concludes that Riyadh's …

Developing Machine Learning And Time-Series Analysis Methods With Applications In Diverse Fields, Muhammed Aljifri

Theses and Dissertations

This dissertation introduces methodologies that combine machine learning models with time-series analysis to tackle data analysis challenges in varied fields. The first study enhances the traditional cumulative sum control charts with machine learning models to leverage their predictive power for better detection of process shifts, applying this advanced control chart to monitor hospital readmission rates. The second project develops multi-layer models for predicting chemical concentrations from ultraviolet-visible spectroscopy data, specifically addressing the challenge of analyzing chemicals with a wide range of concentrations. The third study presents a new method for detecting multiple changepoints in autocorrelated ordinal time series, using the …

Bayesian Estimation Of Hierarchical Linear Models From Incomplete Data: Cluster-Level Non-Linear Effects And Small Sample Sizes, Dongho Shin

Theses and Dissertations

We consider Bayesian estimation of a hierarchical linear model (HLM) from small sample sizes. The continuous response Y and covariates C are partially observed and assumed missing at random. With C having linear effects, the HLM may be efficiently estimated by available methods. When C includes cluster-level covariates having interactive or other nonlinear effects given small sample sizes, however, maximum likelihood estimation is suboptimal, and existing Gibbs samplers are based on a Bayesian joint distribution compatible with the HLM, but impute missing values of C by a Metropolis algorithm via a proposal density having a constant variance while the target …

Title: I: L1-Norm Matrix Completion For Recommender Systems Ii: Conjecturing-Based Classification, Fatemeh Valizadeh Gamchi

Theses and Dissertations

Recommendation systems are essential for providing personalized user experiences, but their performance can be affected by outliers especially in traditional collaborative filtering methods that use the L2-norm. To address this challenge, we developed two new algorithms, SharpEl1rs and SharpEl1rs-Impute, based on the L1-norm to improve resistance against extreme values and effectively handle missing data. Our experimental setting was designed to compare these proposed methods with existing techniques. Then our algorithms are applied to real datasets to assess their performance, with findings indicating that our proposed models offer improved accuracy in some cases and solid performance in others for industrial-scale recommendation …

Redesign, Evaluation, And Validation Of A Commercially Viable High-Resolution Melt Based Mixture Screening Tool, Chastyn Smith

Theses and Dissertations

Analysis of evidentiary samples containing DNA from multiple contributors (“mixtures”) is a time intensive process for a forensic analyst and one where the contributor nature of a sample is not revealed until the end of the traditional forensic workflow. Often, at this stage, retesting or additional testing of mixture samples may not be possible, particularly if the DNA collection device did not preserve the DNA well enough; consequently leaving only trace amounts of a contributor’s DNA present. Thus, a new collection device that would allow for the increased preservation/integrity of evidentiary samples as well as a method that would allow …

The Genetic Architecture Of Cervical Change During Pregnancy: From Modeling To Mechanism — Does The Cervix Mediate Maternal Risk For Spontaneous Preterm Birth?, Hope M. Wolf

Theses and Dissertations

This project leverages clinical data and biospecimens from a prospective longitudinal cohort of pregnant women to study the genetic and phenotypic relationships between cervical shortening and the duration of pregnancy. Sonographic cervical length (CL) was measured throughout pregnancy in a cohort of 5,160 Black/African American women in Detroit, Michigan. Maternal DNA samples were sequenced with a next-generation low-pass whole genome platform. The heritability of cervical change during pregnancy and its genetic correlation with gestational age at delivery (GAD) were estimated using Genome-Wide Complex Trait Analysis. These estimates suggest that cervical change is heritable (h²CL = 51%) and highly polygenic trait. …

Developing A Precision Agriculture Framework To Assess Financial Viability Of Decisions In Farming And Conservation, Jennifer Sublett

Theses and Dissertations

Agricultural producers are invested in managing the impacts of crop damage on their yields and profit. When damage occurs early enough in an agricultural growing season, farmers have the option to replant their corn stand in an effort to recoup some of the lost profits. In this thesis two different types of naturally occurring damage, wildlife depredation and persistent weed or insect patches, were simulated on two representative regions of Mississippi. These data were then used to assess the financial viability of a range of damage mitigation methods, including partial replanting, enrollment into a government conservation buffer, and no action. …