Statistics and Probability Commons^™

A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis

All Dissertations

Real-world materials, particularly biological structures such as feathers exhibit complex appearances that vary spatially across their surfaces. The field of computer graphics provides a means of understanding such surfaces through material modeling which uses both analytical models and data acquired from light-surface interactions. There are many efforts within the past decade in measuring materials for graphics, but common limitations in these works include not accounting for spatially varying properties and reliance on neural networks and synthetic datasets.

Feathers from modern birds present diverse appearances due to how light interacts with their unique hierarchical microstructures. Variations in those structures lead to …

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

Computer Vision In Soccer: Yolov11 Analytics Engine For Quantifying Game Strategy, Connor S. Maurer

Data Science Undergraduate Honors Theses

Single-shot object detection capabilities significantly reduce computational overhead for real-time computer vision in sports analytics at 60 FPS. YOLO11’s lightweight CNN gives promising accuracy while meeting the low-latency demand of dynamic soccer matches. As data-driven approaches take over the sport of soccer, efficient player tracking systems become critical for informing coach’s strategies. I prototype the ETL (Extract, Transform, Load) process of data collected from a single- shot detection program and evaluate its viability for estimating player fatigue. YOLO11 detects players, the ball, and other characteristics, with the output transformed by homography to estimate the positions in the real world. These …

Reinforcement Learning, Modeling Markets, And Professional Basketball Free Agency, Jacob Cohn

Computational and Data Sciences (PhD) Dissertations

This dissertation presents a reinforcement learning-based approach to modeling and optimizing decision-making in professional basketball free agency and related economic environments. A Markov Decision Process (MDP) framework is introduced to capture the strategic interactions of NBA teams bidding for free agents under budgetary and roster constraints. To address computational scalability challenges, a reinforcement learning (RL) environment is developed, leveraging Proximal Policy Optimization (PPO) to approximate optimal policies for team decision-making.

Empirical results demonstrate that the RL agent successfully learns strategic bidding behavior that aligns with dynamic programming benchmarks in simplified settings while scaling effectively to larger, intractable environments. The study …

Impacts Of Cognitive Workload On Veteran Driver Reaction Time: Predictive Modeling Using Bayesian And Machine Learning Methods, Kenneth Ofosu-Kwabe

All Theses

In high-demand environments, the ability to manage cognitive workload can mean the difference between optimal or safe performance and critical failure or accidents. Veterans face an elevated risk of fatal motor vehicle accidents due to post-deployment stress, combat-related injuries, and challenges readjusting to civilian driving. This study explores how cognitive workload affects reaction time performance using a driving simulator by collecting and analyzing subjective workload ratings (using the NASA-TLX survey), physiological signals from eye-tracking and performance data from a sample of 28 Veterans.

We examined how task difficulty, cognitive indicators and personal attributes influence reaction times across an interactive driving …

Deleting Values May Either Increase Or Decrease Variance, David L. Farnsworth

Articles

The impact upon variance when a value is deleted is addressed. It is shown that the cutoff for the deleted value yielding an increase or a decrease in variance is approximately one standard deviation from the mean for a univariate random variable with equally distributed probability on a finite set of elements and for a univariate set of observations. The influence of truncation of the domain for such a discrete random variable and for observations is considered.

Multimodal Benchmarking For Ncaa Basketball, Brendan Barnett

Honors Scholar Theses

We present the first multimodal, multitask benchmark for NCAA basketball, synthesizing structured statistical features with large language model (LLM)-generated game summaries across 19,739 games spanning four NCAA Division I seasons (2021--2025). We evaluate three model families---XGBoost, deep neural networks, and Transformers---under tabular-only and early-fusion settings to measure the impact of LLM-derived textual embeddings. To assess practical utility, we simulate fixed-stake and Kelly criterion-based betting strategies using historical bookmaker odds, analyzing both profitability and downside risk via Monte Carlo simulation. Our results show that XGBoost with early-fusion achieves the highest return on investment and the lowest risk of loss. This work …

Leveraging Historical Data For Estimating Genetic Gain And Implementing Genomic Selection In A Student Led Barley Breeding Program, Sydney Graham

Department of Statistics: Dissertations, Theses, and Student Research

In Nebraska, winter feed barley presents an emerging market for producers and an opportunity to diversify cropping systems. The University of Nebraska Barley Breeding Program aims to develop high-yielding, winter-hardy varieties. A unique aspect of this program is that doctoral students serve as barley breeders and are responsible for crossing, data collection, and advancement decisions. While this provides hands-on experience for the students, the impact of student leadership has not been examined.

This study used a historical data set to evaluate the realized genetic gain of the breeding program, and as a training population for genomic selection. The dataset consisted …

Maximal Independent Set Algorithms Within Procedural Planar Maps: A Large-Scale Evaluation, Chaucer Ihrig

Honors College Theses

Analysis of a childhood game has led us to the problem of maximum independent sets in planar graphs. We wrote a graph creation utility using R to generate a random planar map and its dual graph. This utility then finds a graph’s maximal independent set using a variety of six algorithms. We investigate statistical connections between graph structure, colorability, and the maximal independent sets found using these algorithms over an incredibly large and procedurally generated dataset. We find one can always win the coloring game if the resultant graph is two-colorable. The algorithms perform statistically and practically significantly better on …

Designing Accessible And Dependable Tools For Vocational Rehabilitation Data Analysis, Ruth E. Taylor

All Graduate Theses and Dissertations, Fall 2023 to Present

Since 1973, the U.S. Rehabilitation Services Administration (RSA) has partnered with state vocational rehabilitation (VR) agencies to help individuals with disabilities achieve meaningful employment and independence. RSA-911 datasets play a crucial role in this effort by capturing detailed participant data, but their complexity can hinder effective analysis.

To simplify this process, we present an R software package to streamline the cleaning and analysis of RSA-911 and Transition Readiness Toolkit (TRT) data, a new measure of program effectiveness. We also deliver a user-friendly dashboard, empowering both VR researchers and counselors with the opportunity to conduct analyses. Using our developed tools, we …

Community Voices, Climate Action Choices: Working Towards A Resilient Monterey County, Lesley A. Solano Alonso

Capstone Projects and Master's Theses

Vulnerable communities in Monterey County face disproportionate environmental and health impacts due to climate change, yet many residents remain unaware of the tools and resources available to support local action. This capstone project was implemented in partnership with Ecology Action (EA) and the Resilient Central Coast (RCC) campaign to increase awareness and engagement with the RCC platform. Serving diverse communities across Monterey County, the project included bilingual outreach efforts, community tabling, educational presentations, and a climate action survey. Over 650 residents were engaged directly, resulting in 99 new household sign-ups on the RCC website, a major milestone for the agency. …

A Comparative Analysis Of Nf-Κb1 Gene Regulatory Sequence Methylation In Normotensive And Hypertensive Kenyans, Aaryan Barlas Piracha

Honors Theses

Accounting for the majority of deaths worldwide, non-communicable diseases (NCDs) present the greatest health challenge of the twenty-first century. Specifically, cardiovascular diseases (CVDs) exceed all other NCDs in annual deaths and especially affect low- and middle-income countries (LMICs). Hypertension, being the primary risk factor for CVD, affects over 75% of adults in LMICs due to inadequate health care and preventative measures. Additionally, epigenetic modifications of DNA are important mechanisms that regulate gene expression; DNA methylation, in particular, affects cytosine residues in cytosine-phosphate-guanine (CpG) islands on regulatory sequences. Previous research in our laboratory analyzed percent methylation at 8 different CpG islands …

Analysing Bell Experiments Through Test Factors: Applications To Randomness And Strength Of Nonlocality, Soumyadip Patra

LSU New Orleans Theses and Dissertations

This work presents practical tools to analyse Bell experiments---experiments demonstrating correlations that defy classical explanations and proving that nature violates local realism. We begin by showing that in the Bell scenario specified by n parties with each party having a choice of m binary-outcome measurements---the (n,m,2) scenario---projecting weakly-signalling settings-conditional outcome distributions onto the smallest-dimensional affine subspace (containing the no-signalling set) via an L^2-distance-minimising map preserves correlators. This result ensures that Bell inequalities written in terms of correlators remain invariant under such projections, and we provide an efficient construction method for the projection operator that avoids computationally costly steps such as …

Nonparametric Methods For Bayesian Community Detection In Complex Networks, Kedran Young

Graduate Theses and Dissertations

Network analysis is becoming an increasingly popular interdisciplinary area of study, with emerging interest in fields like sociology, biology, economics, and ecology. Within the niche of network analysis, capturing the community structure of a network is one important achievement that many statisticians have been working toward over recent decades. The most popular modeling technique for latent community detection is the Stochastic Block Model (SBM), which falls into the category of latent variable models and will serve as the baseline model throughout this thesis. SBM is widely regarded as the most effective community detection method as it detects latent community membership …

Analyzing Sleep Staging And Cognitive Transitions Using Fmrl Time Series Analysis, Qingwen Zeng

Arts & Sciences Graduate Student Theses and Dissertations

Understanding sleep stages and their underlying cognitive transitions is essential for advancing our knowledge of brain function. While sleep staging has traditionally relied on electroencephalogram (EEG), this study explores the feasibility of classifying sleep stages using only functional Magnetic Resonance Imaging (fMRI) data. We investigate the use of Hidden Markov Models (HMM) and Hierarchical Dirichlet Process Hidden Markov Models (HDP-HMM) to capture temporal brain-state dynamics from task-free fMRI recordings. A series of pipelines—including sliding window, two-stage majority filtering, and prototype-based mapping via the Hungarian algorithm—were implemented to align model-inferred states with EEG-defined sleep stages. Among the twelve tested pipelines, the …

Decoding The Algorithm: The Mathematics Behind Tiktok’S Short-Form Content Success, Ashley N. Lynch

Honors Scholar Theses

Within the realm of social networks, TikTok has become the central hub for short-form video content. The network’s unique ability to capture individual preferences using predictive analytics has greatly contributed to its massive success, allowing the company to optimize its performance and content personalization. In an age where digital media have such a significant influence on society, it is essential that users develop an understanding of how social network algorithms function to make more informed online decisions. Although TikTok’s technological system is primarily undisclosed, the platform certifiably leverages several key mathematical principles within its algorithm to achieve its core goals …

Investigating Students’ Proficiency Across Statistical Software And Preferences Of Statistical Software Design, Sabrina White

Honors College Theses

This paper investigated students’ perceptions of their proficiency with statistical software applications and their preferences regarding software features. Results indicated that students’ statistical and coding experience, as well as the specific application used, did not significantly influence their self-perceived proficiency. This suggests that it may be more effective to focus on building student skills within a chosen application, rather than tailoring the application to match existing student capabilities. While students showed clear preferences for certain features, favoring clarity over depth, flexibility over safeguards, and built-in checks over unrestricted freedom, these preferences generally leaned toward balanced design rather than extremes. This …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

Application Of Deep Learning On Gage R&R For Anomaly Detection, Oluwatope Richard Ojo

Electronic Theses and Dissertations

This thesis explores the application of deep learning techniques, specifically autoencoder based models, to enhance anomaly detection within Gage Repeatability and Reproducibility (Gage R&R) studies—an essential component of Measurement System Analysis (MSA) in quality engineering. Traditional Gage R&R methodologies, while effective for linear and low-dimensional data, exhibit limitations in detecting subtle, nonlinear variations in complex measurement systems. To address this challenge, an unsupervised autoencoder was developed and trained on a synthetically generated dataset comprising 2,500 voltage measurements (5V and 33V) derived using Generative Adversarial Networks (GANs) based on real-world manufacturing data measurements.

The proposed autoencoder model achieved a 95th percentile-based …

Innovative Methods For The Design And Analysis Of Phase Ii Clinical Trials, Feng Tian

Dissertations and Theses (Open Access)

Drug development has become increasingly time-consuming, costly, and risky in recent years. There is significant potential for improving clinical trial designs, particularly for phase II trials, which play a critical role in the drug development process. Innovative methods are especially necessary for addressing key challenges in phase II trials in terms of dose-ranging study, patient population selection, and decentralized clinical trials (DCTs). This dissertation presents a comprehensive set of methodologies that address these critical issues with three projects. The first project introduces a Bayesian adaptive dose-ranging design that integrates both efficacy and toxicity data to evaluate each dose comprehensively. The …