Statistics and Probability Commons^™

Kernel Density Estimation And Convolution, Nicholas Tenkorang

Open Access Theses & Dissertations

Kernel Density Estimation (KDE) is a widely used technique for estimating the probability density function of a random variable. In this study, we revisit KDE through the lens of convolution and extend this perspective to special cases such as positive, bounded and heavy tailed random variables. Building on this foundation, we propose a novel simulation-based density estimation method that generates new data by adding noise to observed values and then smoothing the resulting histogram using splines. A minor adjustment to natural cubic splines is required to ensure nonnegative estimates. The noise is drawn from a class of bounded polynomial kernel …

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 …

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 …

Yield Prediction Of Pv Solar Energy Systems And Its Application In The Energy Grid For Operational Efficiency, Pablo Bustamante

Open Access Theses & Dissertations

The generation of power from photovoltaic (PV) solar panels is influenced by a multitude of factors. These include the tilt and orientation of the solar panels, the latitude of their location, and the prevailing climate and weather conditions. Additionally, shading at specific locations, particularly if the panels are not part of a solar facility, can significantly impact their efficiency. The quality and efficiency of the panels themselves, along with the preventive maintenance of both the solar panels and associated components such as inverters and trackers, are also critical. Finally, the overall system design and installation play a vital role in …

A Profile Wald Test In M-Estimation, Reagan Kesseku

Open Access Theses & Dissertations

Despite the growing popularity of machine learning-based inference, classical statistical inference remains highly relevant in modern data science due to its interpretability and theoretical rigor. Among its core tools, the likelihood ratio test, Wald test, and score test are foundational methods for hypothesis testing within the maximum likelihood framework. Although these tests are asymptotically equivalent under regularity conditions, each offers distinct advantages depending on the context, computational demands, and the availability of parameter estimates. In this dissertation, we introduce a fourth method, the Profile Wald Test (PWT), within the broader M-estimation framework. The PWT is based on profile estimators of …

Clinicogenomic Insights For Prostate Cancer Progression, Kelvin Ofori-Minta

Open Access Theses & Dissertations

Prostate cancer (PrCa) remains a critical challenge in precision oncology due to several reasons including its apparent heterogenous condition, recurrence following treatment and rapid progressive forms. Therefore, identifying patients at risk of progression is essential to fast-track therapeutic decisions and improve outcomes. Despite recent advances in genomic and molecular profiling, conventional PrCa risk assessment tools heavily rely on a few clinical parameters, neglecting the prognostic potential of genomic biomarkers in the presence of clinical biomarkers. This study presents a computational pipeline to harmonize and evaluate the prognostic value of clinicogenomic profiles of patients in modelling progression free survival (PFS). PFS, …

Correcting Sampling Bias With Privacy-Preserving Synthetic Data: Inference Stability Under The Da-Mi Framework, Hannah Jiang

Arts & Sciences Graduate Student Theses and Dissertations

With the rapid advancement into the Data Age, synthetic data has emerged as a promising avenue for sharing scientific information while protecting the original data. While existing research has primarily focused on generating synthetic data to accurately replicate the characteristics of observed data, we explore the potential of synthetic data to adjust for unrepresentative sampling. This study explores how sampling bias—specifically unbalanced subsets—impacts statistical inference, and whether synthetic data can help correct such bias. Using a Data Augmentation–Multiple Imputation (DA–MI) framework, we generate synthetic datasets from biased samples and evaluate parameter recovery under different correction strategies. Simulations under a Missing …

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 …

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 …

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 …

Aleci: An R Package For Non-Parametric Confidence Intervals On Accumulated Local Effects Plots, Matthew R. Lister

All Graduate Reports and Creative Projects, Fall 2023 to Present

Machine learning models can take a collection of inputs and craft an output. The mathematical formulas these models use to calculate their outputs easily become too complex or time consuming for a human to analyze. Collectively, we refer to these as black box models. Accumulated local effects plots (ALE) are a method for adding interpretability and visibility into the effects that individual variables contribute to the predictions made by black box models. The method designed by D.W. Apley calculates equally spaced point estimates of the response value to construct a graph across the range of the variable of interest. AleCI …

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 …

Nonlinear Power Function Model Changepoint Detection., Jacob Steven Townson

Electronic Theses and Dissertations

Most work surrounding changepoint analysis focuses on linear models. This dissertation explores changepoint detection in nonlinear power function models, specifically focusing on models where the constant multiplier and power are the parameters to be estimated in addition to the changepoint parameter. The study assumes an asymptotic framework as the number of observations approaches infinity. The study explores various model fitting algorithms, and decides to employ the Newton-Raphson method for parameter estimation, with a custom implementation developed to optimize the process. The research first establishes the strong consistency of estimators for the model without a changepoint. Building on this result, consistency …

Joint Modelling Of Longitudinal Egfr Trajectory And Time To Acute Kidney Injury In Lung Transplant Patients, Samiha Zakir

Theses and Dissertations

Progressive declines in estimated glomerular filtration rate (eGFR) often precede acute kidney injury (AKI), yet the relationship between eGFR trends and AKI risk remains unclear. This study investigates longitudinal eGFR changes and their association with AKI in 459 lung transplant patients followed for up to 7 years (n = 6419). We applied a piecewise linear mixed-effects model to evaluate eGFR trajectories and a Cox proportional hazards model to assess time to AKI. A joint model was used to explore the interplay between longitudinal and survival processes. Key covariates included gender, age at transplantation, antibody-mediated rejection (AMR), and pre-transplant eGFR. Males …

Expressive And Interpretable User Engagement Prediction Using Multivariate Survival Processes, Akshay Aravamudan

Theses and Dissertations

The ability to characterize how information diffuses online is of paramount importance to stakeholders that are interested in tasks such as proposing solutions for mitigating and countering dis/misinformation, predicting user engagement of content in social media, planning marketing campaigns to roll-out products and planning dissemination of political campaign messaging among others. One such facet of learning the dynamics of information diffusion is the ability to predict user engagement or the popularity of a single piece of information as it spreads through an online medium. Existing works in this regard mainly either obfuscate user level information or utilize frameworks that are …

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 …

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 …

Optimal Experimental Plan For Multi-Level Stress Testing Under Progressively Hybrid Censoring, David Kojo Amakye

Open Access Theses & Dissertations

Reliability analysis is essential for understanding how products perform over time, particularly in environments where failure data is limited or costly to obtain. One effective approach is multi-level stress testing, where test units are subjected to varying levels of stress to accelerate failures and extract more information within constrained timeframes. This study presents a novel optimization-based framework for designing life-testing experiments under progressively Type-II hybrid censoring, assuming Weibull lifetime distributions. Leveraging a Variable Neighborhood Search (VNS) algorithm, we determine efficient allocations of test units and censoring parameters across multiple stress levels to enhance the precision of estimates of the model …

Optimal Accelerated Life-Testing Plans Under Progressive Type Ii First Failure Censoring Scheme, Emmanuella Duah

Open Access Theses & Dissertations

Designing optimal accelerated life testing (ALT) plans under progressive Type-II first failure censoring involves complex computational challenges, especially when trying to balance efficiency, precision, and practicality. This research introduces a novel optimization framework aimed at determining the best test configuration that minimizes estimation uncertainty within constrained experimental conditions. We developed a tailored meta-heuristic strategy based on an enhanced Variable Neighborhood Search (VNS) algorithm, which efficiently navigates the complex landscape of censoring schemes and stress allocations. Unlike conventional methods that typically focus on simpler censoring or stress-level structures, this approach simultaneously optimizes both the censoring points and sample allocations across various …

Computing Optimal Progressive Hybrid Censoring Schmes Using An Mcmc Type Probabilistic Approach, Irene Yemotiorkor Odoi

Open Access Theses & Dissertations

Progressive hybrid censoring schemes play a crucial role in optimizing life-testing experiments by balancing test duration and statistical efficiency. This study presents a Markov Chain Monte Carlo (MCMC)-based probabilistic approach for determining optimal progressive hybrid censoring schemes, incorporating a time-dependent component that enhances traditional progressive censoring methods.We implement our approach using three distinct probability distributions the multinomial, hypergeometric, and uniform distributions to simulate censoring schemes. The optimal censoring schemes are then identified based on three optimality criteria: A-optimality, D-optimality, and T-optimality, ensuring robust selection by minimizing estimator variance, maximizing Fisher information, and optimizing test duration, respectively..To evaluate the effectiveness of …

Computing Optimal Multi-Level Stress Testing Plans Using A Combined Variable Neighborhood Search Algorithm Under Progressive Type-Ii Censoring Scheme, Michael Obuobi

Open Access Theses & Dissertations

In multi-level stress life tests under Type-II progressive censoring, determining optimal allocation poses significant computational challenges due to the vast solution space. Efficient methods are essential for exploring the admissible censoring schemes effectively. This thesis introduces a novel meta-heuristic algorithm, the Combined Variable Neighborhood Search (CVNS), which computes optimal schemes at different stress levels simultaneously. Unlike methods focusing on marginal stress levels or one-step progressive censoring, this approach leverages a unified framework to ensure enhanced computational efficiency and solution quality. By integrating the components of the design parameters into a cohesive optimization process, the algorithm effectively reduces computational time while …

A Study Of End-Cut Preference In Tree-Based Modeling, Xiangya Wang

Open Access Theses & Dissertations

Decision trees, particularly those built using the Classification and Regression Trees (CART) algorithm, are widely used for their interpretability and flexibility. However, the greedy nature of the CART splitting procedure gives rise to the end-cut preference (ECP) phenomenon, wherein split points near the extremes of predictor ranges are favored. This study offers a comprehensive investigation of ECP, exploring its theoretical underpinnings, practical manifestations, and implications for both single decision trees and ensemble methods such as Random Forests. Through theoretical analysis and simulation studies, we examine how ECP affects tree structure, variable selection, and predictive accuracy across tree-structured, linear, and nonlinear …

Car Price Prediction Using Machine Learning: Analyzing The Dvm-Car Dataset, Yaman Abu Ghareebaih

Electronic Theses and Dissertations

The objective of this study is to predict car prices using machine learning models and the DVM-CAR dataset, which includes over 1.4 million images and car specifi- cations from 899 car models. Key factors such as mileage, engine power, and year of registration were analyzed for their correlation with car prices. Extensive data cleaning was performed, including filling missing values, identifying outliers, and normalizing numerical variables. Discrete variables like car make and body type were encoded using one-hot encoding. Linear relationships were analyzed with Multiple Logistic Regression, and Random Forest models were used for nonlinear patterns. Model performance was evaluated …

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. …

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 …

Exploring Latent Mediation Through Bayesian Regularization Methods Of Lasso, Ridge, Horseshoe, Spike-And-Slab, Ethan Harris

Graduate Theses and Dissertations

Regularization is a powerful tool to combat overfitting and drive sparsity in complex models. Regularization was initially applied in regression modeling but has been increasingly utilized in structural equation modeling where its utility in identifying the essential components has helped improve modeling. As structural equation models have increased in complexity both in the number of indicators but also the number of latent factors, researchers have begun to investigate how applying Bayesian regularization to these systems can further push the limits on modeling complex models with limited sample sizes. One area where research is limited is the application of Bayesian regularizations …

New Bayesian Methods For Longitudinal Data Analysis With Complex Dependence Structures., Anish Mukherjee

Electronic Theses and Dissertations

Longitudinal data in real-world settings are frequently found to be heterogeneous and exhibit intricate spatio-temporal dependence structures. Analyzing such complex data to obtain reliable estimation while quantifying uncertainty necessitates using sophisticated Bayesian methodology. In this work, we present novel Bayesian methods developed to address these challenges. We often observe heterogeneity in longitudinal data, where the mean and variance for certain profiles meaningfully differs from the rest. Some profiles may also exhibit outliers at a limited number of measurements. Using a standard mixed effects model, which assumes homogeneity, can lead to overestimating the residual variance and inefficient estimation. In this work, …

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 …

Dual-Criterion Dose Finding Designs For Phase I Clinical Trials, Yunlong Yang

Dissertations and Theses (Open Access)

The primary objective of Phase I oncology trials is to assess the safety and tolerability of novel therapeutics. Conventional dose escalation methods identify the maximum tolerated dose (MTD) based on dose-limiting toxicity (DLT). However, as cancer therapies have evolved from chemotherapy to targeted therapies, these traditional methods have become problematic. Many targeted therapies rarely produce DLT and are administered over multiple cycles, potentially resulting in the accumulation of lower-grade toxicities, which can lead to intolerance, such as dose reduction or interruption. To address this issue, we proposed dual-criterion designs that find the MTD based on both DLT and non-DLT-caused intolerance. …