Statistics and Probability Commons^™

Leveraging Deep Learning Recurrence And Attention Mechanisms For Flood Forecasting And Assessment, Elnaz Heidari

All Dissertations

Predicting how much water will flow in rivers and streams is important for managing floods, water supply, and the environment. Traditionally, government agencies have used complex models, such as the National Water Model (NWM), which simulate how much water moves through landscapes using physical laws and real-world data. However, recent advances in Artificial Intelligence (AI) have enabled new ways to make these predictions. This research explored whether AI-based models could predict river discharge more accurately. These AI models learn patterns from past data instead of relying only on physical rules. To find out how well they work, the AI models …

A Longitudinal Analysis Of Hospital Consumer Evaluation In Virginia, Tulay Akmandor Inac

Health Services Research Dissertations

Suboptimal patient experience signals a need to improve clinical efficacy, patient safety, and healthcare quality. The COVID-19 pandemic intensified hospital resource and staffing demands, reducing hospitals’ capacity to invest in patient experience improvement. Prior studies remain limited because many lack longitudinal structure and organized theoretical models, making temporal inference difficult and weakening analyses of patient experience disparities. To address these limitations, this dissertation incorporates three studies examining patient experience and pandemic-related effects.

In state-level markets comparable to Virginia, limited research has examined longitudinal patient experience trends across regional hospital systems using HCAHPS scores. The first study uses descriptive trend analysis …

Unifying And Expanding Global And Local Variable Importance Methods For Explainable Machine Learning, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning methods are powerful analytical tools used across all scientific disciplines and many other fields of investigation for prediction and inference from diverse data sources. Despite their broad applicability, machine learning methods are often highly complex and difficult to interpret. Developing a greater understanding of which variables most influence a response is essential for increasing the interpretability of these models and supporting informed decision-making. This research focuses on improving how we evaluate the importance of these variables.

One common approach is to shuffle the values of a variable and see how much the model accuracy gets worse. Another approach …

Learning Latent Structure In High-Dimensional Data Via Geometry And Graphs, Haozhe Chen

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern datasets often contain many measured variables for each observation, such as gene-expression levels, brain activity signals, or features in tabular data. These data are also often noisy, meaning that useful patterns are mixed with measurement error or irrelevant variation. Although such datasets can appear complex, they are frequently represented by simpler hidden structures, such as trajectories, clusters, or relationships between observations. This dissertation develops methods for uncovering these hidden structures by learning geometric and graph-based representations directly from data. The first part introduces Functional Information Geometry, which represents local patterns in high-dimensional data using functional features and constructs a …

Mapler: An R Package For Estimating The Impact Of Climate Change On Maple Syrup Production, Matthew T. White

All Graduate Theses and Dissertations, Fall 2023 to Present

Successful maple sap tapping depends on the freeze/thaw cycle (i.e., temperatures fluctuating above/below freezing) during the winter and spring. Climate change threatens to alter the timing and duration of the tapping season. This necessitates research into how maple sap tapping will be impacted by climate change in order to help maple syrup producers prepare for the future. We define a sap day as a day where the freeze/thaw cycle occurred. Using information climate scientists use to predict future temperatures, we calculate how many sap days could occur each year. We develop software to analyze these sap day calculations to determine …

Modeling Mean And Variability Of Anxiety In Ecological Momentary Assessment Data Using Mixed-Effects Location–Scale Models, Trenzy Odero

Electronic Theses and Dissertations

Ecological Momentary Assessment is a method of collecting repeated measures of people in real time within natural environments. This results in hierarchical data that has a significant amount of variation at the person level. The traditional linear mixedeffects models assume that the residual variance is constant, which might not be true when the residual variance varies among individuals as well as in time. This thesis uses mixed-effects location-scale (MELS) models to model the mean and variance of an EMA outcome together. By introducing the possibility of variability in residual variance within and across individuals and with covariates, the MELS framework …

When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto

Research Collection School of Social Sciences

Despite the use of latent growth mixture modelling (LGMM) to study longitudinal changes, existing practices may inadvertently impede this very investigation. Although subgroup trajectories may theoretically differ in their structure (e.g., some subgroups being linear, some curvilinear), the current convention advocates overreliance on the baseline model to derive subsequent profile trajectories, which may obscure these structural differences. In this article, we provide a brief description of extant LGMM practices, after which we explicate the pitfalls of the current approach. Finally, we provide a principled approach for LGMM research moving forward. Specifically, we recommend specifying a set of theoretically plausible models …

Evaluating Machine Learning Models On Classification Of Novel Cyber Attacks In The Healthcare Domain, Promise Ehimen

Dissertations, Theses, and Projects

The increasing adoption of the Internet of Medical Things (IoMT) has improved healthcare delivery through connected medical devices while simultaneously expanding the cybersecurity risks facing healthcare organizations. Although machine learning based intrusion detection systems have demonstrated high detection accuracy, their ability to respond reliably to previously unseen cyberattacks remains uncertain. This study investigated how a Neural Network model and a Logistic Regression model classified novel cyberattacks within the IoMT environment. The Neural Network and Logistic Regression models were both trained and tested using a subset of the CICIoMT2024 benchmark dataset. The Neural Network achieved 99.82% test accuracy and a 0.94 …

A Mathematical Decision-Making Framework For Athlete Development In A Collegiate Taekwondo Community: Prioritizing Coaching Interventions Using Statistical Analysis And The Analytic Hierarchy Process, King Harold A. Recto, Hazel Jade L. Antonio, Jhyrald Anthony P. Dalida

Electronics, Computer, and Communications Engineering Faculty Publications

Athlete development within collegiate sports communities requires informed decisions regarding the prioritization of coaching interventions and allocation of developmental resources. However, such decisions are frequently guided by experience and intuition, limiting opportunities for systematic and evidence-based decision-making. This study develops a mathematical decision-making framework for athlete development by integrating statistical analysis and the Analytic Hierarchy Process (AHP) within a collegiate taekwondo community. Data were collected from 25 collegiate taekwondo athletes who satisfied established eligibility criteria, including participation in University Athletic Association of the Philippines (UAAP) competitions during the previous three seasons. Athletes evaluated coaching practices across five dimensions: Training and …

Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman

Biomedical Sciences ETDs

Early life adversity (ELA) increases lifelong neuropsychiatric vulnerability. Yet how ELA reorganizes brain-wide activity and circuit coordination across later experience remains unclear. This dissertation tests the hypothesis that ELA alters adult brain-wide activity and responses to threat through disrupted coordination among neural systems that regulate emotional experience, including prefrontal-limbic and monoaminergic systems. Longitudinal manganese-enhanced MRI of adult mice exposed to standard or fragmented early care, combined with computational processing and statistical modeling, quantified brain states before, during, and long after innate predator threat. These studies established that acute threat evokes large-scale, distributed brain activity that evolves over time. ELA potentiates …

Interpretable Case-Control Inference Through Log-Linear General Location Models, Zacharia Stuart

Mathematics & Statistics ETDs

This dissertation analyzes one of the few publicly available NFL injury datasets to study field type and non-contact lower-limb injuries. Field type is studied jointly with other risk factors to understand how these factors interact to affect injury risk. The data were gathered through a case-control sampling scheme, which limits direct inference on absolute injury probabilities. While not the most common approach for case-control data, this dissertation models the retrospective distribution directly through Log-Linear General Location Models (Log-Linear GLOMs). Through a log-linear structure placed on a log-odds-ratio reparameterization, the model provides directly interpretable marginal and interaction contributions to injury log-odds …

The Uncertainty Principles, Lee Michael Felicetti

Mathematics & Statistics ETDs

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

Volatility Spillovers Between Stock Prices And Exchange Rates: Insights For Risk Management And Investment Strategies: Evidence From China, India, And Pakistan Using Bekk-Garch Models, Samreen Fatima, Humera Sultana, Muhammad Najamuddin Dr., Saba Naz

The Indonesian Capital Market Review

This study investigates the dynamics of volatility and its spillover effects between the stock markets of China, India, and Pakistan, and their respective exchange rates (USD/CNY, USD/INR, and USD/ PKR). Volatility is modeled using the Symmetric and Asymmetric BEKK-GARCH (1,1) and DCCGARCH (1,1) models, based on daily return series covering the period from January 1, 2019, to January 31, 2025. The empirical results indicate that both the employed models are adequate for capturing the volatility dynamics. The findings reveal that the highest value of portfolio weights and hedging efficiency of KSE-100 Index–USD/PKR provide optimal portfolio allocation and highest hedging performance …

Quantitative Methods In Education: A Practical Introduction To Statistics, Yukiko Maeda, John Gipson, Sheila Hurt, Katie H. Dufault

Purdue University Press Books

Educational research often involves understanding complex patterns in student achievement, teacher effectiveness, and institutional performance. Quantitative Methods in Education: A Practical Introduction to Statistics is designed to equip current and future educators and researchers with a basic comprehension of the statistical tools necessary to effectively analyze and interpret educational data. In today’s data-driven world, the ability to leverage statistical techniques is essential for making informed decisions that can enhance learning outcomes and maximize learner potential. This book provides a systematic approach to exploring these trends using both descriptive and inferential statistics, providing readers with the knowledge to conduct rigorous analyses …

Feasibility And Acceptability Of Automated Texts To Offer, Screen, And Enroll Patients In A Cancer Clinical Trial Financial Reimbursement Program: Mixed Methods Study, Ashley E Santaniello, Hena Patel, Sarah Milinski, Mohan Balachandran, Vivian Nguyen, E. Paul Wileyto, Robert H. Vonderheide, Dana Dornsife, Robert G. Johnson, Carmen E. Guerra

Student Papers, Posters & Projects

BACKGROUND: Out-of-pocket (OOP) costs pose a significant barrier to participating in cancer clinical trials (CCTs). Financial reimbursement programs (FRPs) that reduce the burden of OOP costs can support participation in CCTs if the information is readily available to participants at the time of enrollment. Prior studies have shown the importance and impact of FRPs, but despite improvements, significant barriers still remain.

OBJECTIVE: This study was designed to explore the feasibility and acceptability of automated texts designed to offer, screen, and enroll CCT participants in an FRP for OOP travel and lodging-related clinical trial costs.

METHODS: This study used a mixed …

Urban Carbon Emission Early Warning Research Based On The Dpsir Framework And Deep Learning, Xiaochun Zhao, Lingyang Xu, Ying Zhou

Journal of Scientific Information Research

[Purpose/significance] In line with the national requirements for building a carbon emission early warning mechanism, conducting the urban carbon emission early warning research is of great significance for achieving the “dual-carbon” goals. [Method/process] This paper selected 16 prefecture-level cities in Anhui Province as research samples. A carbon emission early warning indicator system was constructed based on the DPSIR framework. By using data from urban statistical yearbooks, the LSTM model was employed with parameter optimization via genetic algorithms to forecast various early warning indicators for 2024-2025.On this basis, a combined subjective-objective weighting method was then applied to calculate the urban carbon …

A Multi-Dimensional Analysis Of China's Future Industry Development Policy Documents, Tianxiang Yao, Wang Xu

Journal of Scientific Information Research

[Purpose/significance] Future industries are important carriers of new quality productive forces which can play a leading role in the economic and social development. Quantitative analysis and evaluation of China's future industry policies can provide support and reference for the formulation, optimization and adjustment of subsequent policies. [Method/process] Taking a total of 84 policy texts at the central, provincial, municipal and county levels in China as the research objects, a three-dimensional analysis framework of "theme-tool-effectiveness" was constructed. By comprehensively applying LDA thematic analysis, content analysis and PMC index model, theme distribution, content characteristics and comprehensive effectiveness of policy texts were deeply …

P-Value Visualizer, Manish Rami

Software

An interactive tool demonstrating what a user set p-value indicates with regards to probability.

Effect Size & Distributional Overlap Visualizer, Manish Rami

Software

An interactive tool comparing a control group and a treatment group, both with standard scores (M = 100, SD = 15). Cohen's d is expressed in standard deviation units. The three shaded regions show what each group's distribution looks like and how much they overlap. You can either use the preset buttons for effect sizes (SLP benchmarks) or the slider to change the values of Cohen's d to examine the distributions.

Existence And Uniqueness Of Positive Solutions For Hilfer–Hadamard-Type Fractional Differential Equations With Γ-Concave And Sub-Homogeneous Operators, Hasan Rasouli, Hojjat Afshari, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

In this research, we present necessary and sufficient conditions for the existence and uniqueness of positive solutions for a class of Hilfer–Hadamard-type fractional differential equations with boundary value problems, including those with integral boundary conditions. The obtained results are conditional on a specific set of strong assumptions, which substantially narrow the class of admissible nonlinearities, coefficients, and boundary data. Thus, the present work extends the Hadamard-type framework to the Hilfer–Hadamard setting only within this restrictive regime, rather than providing a full extension to all Hilfer–Hadamard systems. We utilize the properties of (Formula presented.) -concave and sub-homogeneous operators along with two …