Statistics and Probability Commons^™

Effects Of Chain Length, Saturation, And Bases On Saponification, Sarah Fenik

Williams Honors College, Honors Research Projects

This project will analyze the effects of chain length and saturation of fatty acids on saponification processes, as well as the effects of the base used in the reaction. Stearic acid, lauric acid, and oleic acid will be used for the fatty acid comparisons, and sodium hydroxide and potassium hydroxide will be used for the base comparisons. Stearic acid is considered a long chain fatty acid, while lauric acid is considered a short chain fatty acid. Oleic acid is a monounsaturated fatty acid. Five soap products are be made: sodium stearate, sodium laurate, sodium oleate, potassium stearate, and potassium oleate. …

An Insight Into Mediation Analysis, Nicholas Mccracken

Williams Honors College, Honors Research Projects

Mediation is an ideology often present in the social sciences. A mediator is meant to serve as the middle point between one party and another, taking the communications from one party and ensuring that the other party can comprehend that of the original party. Though this is very popular in social sciences, we can apply a statistical concept to it as well. We can explain the relationship between two parties and a mediator through a series of statistical equations, known as Baron and Kenny’s Equations. With these equations, we can determine how one variable is meant to impact another variable …

Analyzing Car Theft Trends In Central Texas: A Comparative Study Of Waco, College Station, And Killeen, Daniel Njogu

Williams Honors College, Honors Research Projects

This study examines motor vehicle theft (MVT) trends from 2019 to 2023 in three Central Texas cities—Waco, College Station, and Killeen—using temporal analysis, geospatial hotspot mapping, and make/model data. In Killeen, thefts generally rose over the period, with notable peaks in October and on Mondays. College Station saw an overall decline in thefts but experienced a seasonal spike each March, and Waco’s thefts increased until around 2021 before beginning to fall. Local festivals—such as the Spirit of Texas in College Station and the Heart O’ Texas Fair in Waco—appear to coincide with these seasonal upticks. Hyundais and Kias were most …

Analysis Of Public Acceptance Of Urban Air Mobility (Uam) Based On Air Travel Frequency, Seuggyun Jin, Kim O. Chambers

Journal of Aviation/Aerospace Education & Research

Urban Air Mobility (UAM) is an innovative air transportation system designed for efficient travel in urban and suburban areas, offering significant time saving compared to traditional ground transportation. However, concerns about UAM services, such as safety and noise, remain prominent. Understanding public acceptance of UAM is crucial to identifying potential customers and ensuring the sustainability of commercial UAM operations. This study utilizes an online survey from a total of 254 consumer attitudes on the scales of reliability, usefulness, behavioral intention, safety, and concerns to examine public acceptance of UAM based on people's air travel frequencies. Using a one-way ANOVA, the …

Hymate: A Hybrid Mamba And Transformer Model For Ehr Representation Learning, Md Mozaharul Mottalib, Thao-Ly Phan, Rahmatollah Beheshti

Department of Medicine Faculty Papers

Electronic health Records (EHRs) have become a cornerstone in modern-day healthcare. They are a crucial part for analyzing the progression of patient health; however, their complexity, characterized by long, multivariate sequences, sparsity, and missing values-poses significant challenges in traditional deep learning modeling. While Transformer-based models have demonstrated success in modeling EHR data and predicting clinical outcomes, their quadratic computational complexity and limited context length hinder their efficiency and practical applications. On the other hand, State Space Models (SSMs) like Mamba present a promising alternative offering linear-time sequence modeling and improved efficiency for handling long sequences, but focus mostly on mixing …

Extremal Trees For Random Walks, Ben Bridenbaugh

Mathematics, Statistics, and Computer Science Honors Projects

A random walk is a sequence of adjacent vertices that are chosen uniformly at random from the neighbors of the previous vertex. An access time is the average length of time that a random walk takes to reach a target probability distribution from a starting probability distribution, given an optimal stopping rule. This paper deals with characterizing the trees of diameter d and on n vertices that extremize three different types of access times.

Methods In Statistics, Machine Learning, And Deep Learning For Combining Multi-Omics Dataset, Md Mutasim Billah

Dissertations, Master's Theses and Master's Reports

Transcriptome-wide association studies (TWAS) have emerged as a powerful strategy to bridge genome-wide association studies (GWAS) with gene regulatory mechanisms by integrating genotypic data with gene expression data. While early TWAS methods typically rely on linear models and single-tissue expression references, recent advances underscore the need for flexible, multi-tissue approaches that can capture heterogeneous regulatory architectures and tissue-specific expression patterns. This dissertation introduces a three‑part research project that advances multi‑tissue transcriptome‑wide association studies (TWAS) along complementary axes of methodology, statistical power, and modelling flexibility.

In chapter One, TWAS‑CTL introduces a two‑stage cross‑tissue learner that trains any user‑chosen single‑tissue imputers (STLs) …

Comparative Efficacy Of Hallucinogens In Treating Mood Disorders Through A Meta-Analysis Of Symptom Reduction, Dosage, And Duration, John Marco D.F. Muniz

Honors Undergraduate Theses

Background: Hallucinogens including psilocybin, lysergic acid diethylamide (LSD), ketamine, N,N-dimethyltryptamine (DMT) (as ayahuasca), have re-emerged as potential rapid-acting treatments for mood disorders. We conducted a meta-analysis of placebo-controlled trials evaluating their efficacy in depression and anxiety disorders. Methods: A systematic review identified 12 trials (Total ≈ 670) meeting inclusion criteria (randomized, placebo-controlled). Data on Cohen’s d and Hedges’ g effect sizes for depression- and anxiety-related outcomes were extracted. We computed pooled effect sizes (weighted by sample size and inverse variance), performed subgroup analyses by drug, diagnosis, follow-up duration, and outcome measure type, and assessed heterogeneity (I², Q …

A Time Series Analysis Of The Macroeconomic Indicators, Mia Houston

Honors Undergraduate Theses

Understanding inflation—particularly across regions and categories—is crucial for effective policymaking, strategic business decisions, and safeguarding vulnerable populations, as it highlights the diverse drivers and impacts of price changes within the economy. This has become increasingly crucial in recent years between the volatile inflation conditions introduced by the COVID-19 pandemic, energy price shocks, and renewed trade tensions and tariffs. This thesis analyzes 77 U.S. monthly inflation time series from 2003 to 2023 using two forecasting approaches: an elementwise Seasonal Autoregressive Integrated Moving Average (SARIMA) model and a Factor-Augmented Vector Autoregressive (FAVAR) model. The data obtained from the Bureau of Labor Statistics …

Solvability Of Stochastic Linear-Quadratic Optimal Control Problems Under Partial Stabilizability Conditions, Al-Sadh Rahman Imadh

Honors Undergraduate Theses

Optimal Control Theory, a branch of Control Theory, is applicable in fields such as engineering, operations research, and economics. Stochastic Optimal Control deals with noisy systems and data using Ito’s formulation. Given a noisy system and a cost functional, the goal is to find a control that will minimize the cost. This thesis focuses on linear quadratic stochastic optimal control, and we explore state equations that are not stabilizable. We first address measurability concerns arising from the semigroup property of the state trajectory. The notions of partial stability and partial stabilizability are introduced, and we formulate their corresponding Lyapunov and …

Theoretical Analysis Of Cnns For Automatic Seizure Detection In Eeg Signals, Jackson T. Small

Honors Undergraduate Theses

Epilepsy is a common brain disorder where neurons in the brain rapidly fire, causing recurring seizures. The brain activity during a seizure can be detected by electroencephalogram (EEG) signals; however, this process is not only labor-intensive and time-consuming but is also subject to inter-rater variability, with a study showing only moderate agreement when diagnosing patients, even among experts. Convolutional Neural Networks (CNNs) are often proposed to detect seizures automatically, achieving high performance. The focus on performance comes at a cost of losing interpretability, leaving the model as effective but seen as a ’black box’. This thesis confronts the interpretability knowledge …

Role Of C4 Resources In Isotopic Variability In Diet Among Children From Kellis 2 Cemetery, Dakhleh Oasis, Egypt, Faith R. Hendrix

Honors Undergraduate Theses

Using stable carbon isotope analysis, this study investigates dietary diversity in children buried at the Kellis 2 Cemetery (c. AD 50–450) in Egypt's Dakhleh Oasis. From the analysis of δ¹³C isotope values in hair keratin and bone collagen, the study reconstructs short-term and long-term dietary signals in juvenile and adult subjects. The aim is to clarify the role of C₄ plants—particularly millet—in weaning and childhood diets in a Romano-Christian Egyptian village context. A total of 631 segmented hair and 54 bone collagen samples were analyzed from 127 juveniles and 97 adults. Juvenile individuals (i.e., under 15 years biological age) showed …

Partisan Divides In Environmental Spending Attitudes: A Two-Level Hierarchical Analysis, 1973-2022, Jordan Lipner

Honors Undergraduate Theses

Public attitudes toward environmental spending have become increasingly divided along party lines, with sharp shifts over the past five decades. This thesis updates and expands on Johnson and Schwadel’s 2019 study by applying a two-level hierarchical linear model to General Social Survey data updated to include data from 2015-2022, capturing how political affiliation, education, race, and economic context interact with broader political and economic contexts to shape environmental attitudes over time.
The results show that political affiliation remains the strongest and most reactive predictor of environmental spending attitudes. Republican respondents are significantly more likely to oppose environmental spending, especially under …

“Regression To The Mean”: The Confluence Of Eugenics And Statistics In The 19th And 20th Centuries, Emrys G. King

Pomona Senior Theses

The work of this thesis is twofold — first, qualitatively characterizing the confluence between the British eugenics and statistics movements in the late 19th and early 20th centuries, and second, quantitatively analyzing the effect of this foundation on pedagogical materials in the growing field of statistics between 1880 and 1970. Towards the first goal, the history of the method of least squares, state statistics, and positive and negative eugenics are outlined, followed by a close reading of the foundational texts authored by Francis Galton and Karl Pearson that introduced linear regression. Towards the latter goal, English-language statistics textbooks published between …

A Bayesian Complex-Valued Latent Variable Model Applied To Functional Magnetic Resonance Imaging, Chase J. Sakitis, D. Andrew Brown, Daniel B. Rowe

Mathematical and Statistical Science Faculty Research and Publications

In linear regression, the coefficients are simple to estimate using the least squares method with a known design matrix for the observed measurements. However, real-world applications may encounter complications such as an unknown design matrix and complex-valued parameters. The design matrix can be estimated from prior information but can potentially cause an inverse problem when multiplying by the transpose as it is generally ill-conditioned. This can be combat by adding regularizers to the model but does not always mitigate the issues. Here, we propose our Bayesian approach to a complex-valued latent variable linear model with an application to functional magnetic …

Sealing The Deal: A Case Study Of A Private, Southeastern, Regional College’S Student Onboarding Practices, Alicia R. Gaston, Kristen Meyer, Tyler Ogden, Jennifer Perkinson, Casey Yocum Michaels

Doctor of Education Capstones

Each year, higher education institutions offer support to new, incoming students through an onboarding process that requires dedication and collaboration across multiple departments. Offering streamlined guidance and clear communication throughout the onboarding process is essential to ensure incoming students understand action steps without becoming overwhelmed with new terminology, processes, and environments. This explanatory case study is set to understand the current communication practices and technology use across onboarding departments at Brightside College – also referred to as Brightside or BC (pseudonym). The research team aimed to understand Brightside's onboarding staff's perspective of current processes and practices. With emphasis on the …

Maternal Vulnerability Index And Severe Maternal Morbidity, Nansi S. Boghossian, Joshua Radack, Molly Passarella, Ciaran S. Phibbs, Lucy T. Greenberg, Jeffrey S. Buzas, George R. Saade, Jeannette Rogowski, Scott A. Lorch

Faculty Publications

Importance: Few studies have investigated the association of composite measures of neighborhood social determinants of health with severe maternal morbidity (SMM), and no research has examined this association for indices tailored to maternal health. Objective: To examine the association of scores in the Maternal Vulnerability Index (MVI), a tool developed to measure maternal risk of adverse health outcomes, with SMM. Design, Setting, and Participants: This retrospective, population-based cohort study was conducted in 5 states (2008-2020 for Michigan, Oregon, and South Carolina; 2008-2018 for Pennsylvania; and 2008-2012 for California) among individuals delivering a fetal death or a live birth between 22 …

Caregiving Burdens Of Task Time And Task Difficulty Among Paid And Unpaid Caregivers Of Persons Living With Dementia, Matthew Lee Smith, Jodi L. Southerland, Malinee Neelamegam, Gang Han, Shinduk Lee, Chung Lin Kew, Juanita Dawne R. Bacsu, Elyse Couch, Steffi M. Kim, Monique J. Brown Ph.D., Mph, Ayse Malatyali, Lucas Wilson, Zahra Rahemi, Jeremy Holloway, Marcia G. Ory

Faculty Publications

Background: Demands of caregivers of persons living with dementia (PLWD) are often influenced by the context of their caregiving situation. This study examines common and unique factors associated with caregiving burden in terms of task time and task difficulty among paid and unpaid caregivers of PLWD. Methods: Cross-sectional baseline survey data were analyzed from 107 paid and unpaid caregivers of PLWD participating in a larger NIH-funded study assessing the feasibility of using a novel in-situ sensor system. Oberst Caregiving Burden Scale constructs of task time and task difficulty served as dependent variables. Two least squares regression models were fitted, controlling …

Investing In The Development Of The Next Generation Of Mch Leaders, Karen A. Mcdonnell, Jamal Percy, Lisa Anders, Monique J. Brown Ph.D., Mph, Alice R. Richman, Julianna Deardorff, Monica S. Ruiz, Jihong Liu Sc.D., Kelli Russell, Audrey Snyder, Cassondra Marshall

Faculty Publications

The public health landscape is constantly evolving to address the strengths and needs of the community. Training for the public health workforce is leading the way, establishing an ecosystem approach that integrates individuals within social, political, and environmental contexts to promote health equity within a framework of social justice. One area of public health that is innovatively preparing the next generation of leaders is maternal and child health (MCH). In the United States, key indicators of health disparities within MCH remain stagnant, highlighting the need for training programs that develop future MCH professionals from diverse backgrounds. These professionals will deliver …

Healthcare Providers’ Perspective On Hiv Testing And Hypothetical Mhealth-Connected Linkage To Care Among Men Who Have Sex With Men (Msm) In South Carolina, Tony Brown, Prince Nii Ossah Addo, Monique J. Brown Ph.D., Mph, Xiaoming Li, Oluwafemi Adeagbo

Faculty Publications

Background: HIV continues to be an important public health concern in South Carolina (SC). However, an examination of providers’ willingness to use mHealth technologies to address ongoing barriers to HIV care and prevention strategies, particularly among men who have sex with men (MSM) is currently lacking in SC. We therefore explored HIV care providers’ perceptions of HIV testing and treatment uptake among MSM, and providers’ willingness to use mHealth technology to address barriers to HIV testing and treatment in SC. Methods: Between August and December 2021, we conducted semistructured virtual interviews with 10 HIV care providers recruited purposively based on …

Sars-Cov-2 Detection And Persistence In A Remote Amazonian Settlement, Glauco M. Silva, Roberto C. Ilacqua, Franciely G. Gonçalves, Carla M. Santana, Felipe T. Jordão, Paula R. Prist, Melissa S. Nolan Ph.D., Mph, Andreia F. Brilhante, Marcia A. Sperança, Gabriel Z. Laporta

Faculty Publications

Background: COVID-19 continues to pose a major global health challenge. Despite its geographic distance from Brazil’s major urban centers, Acre state has experienced notable outbreaks. This study assessed the detection and persistence of SARS-CoV-2 in the rural settlement of Santa Luzia, located in the remote municipality of Cruzeiro do Sul, Acre state, Brazil. Methods: In July 2022, a cross-sectional survey was conducted at 40 sites from an ongoing environmental study, selected by deforestation patterns and proximity to health posts. Saliva samples were collected from residents aged 5–90 years, followed by nucleic acid extraction and multiplex RT-qPCR for SARS-CoV-2 detection. Results: …

A Method For Empirically Assessing Small Area Estimators Via Bootstrap-Weighted K-Nearest-Neighbor Artificial Populations, With Applications To Forest Inventory, Grayson W. White, Jerzy Wieczorek, Zachariah W. Cody, Emily X. Tan, Jacqueline O. Chistolini, Kelly S. Mcconville, Tracey S. Frescino, Gretchen G. Moisen

Faculty Journal Articles

National Forest Inventories monitor forest attributes across a variety of spatial and temporal scales in a given country. Increased interest in reporting and management at smaller scales has driven National Forest Inventories to investigate and adopt small area estimation (SAE) due to the promise of increased precision at these scales. However, comparing and evaluating SAE models for a given application is inherently difficult. Typically, many areas lack enough data to check unit-level modeling assumptions or to assess unit-level predictions empirically; and no ground truth is available for checking area-level estimates. Design-based simulation from artificial populations can help with each of …

Small Area Estimation Of Forest Biomass Via A Two-Stage Model For Continuous Zero-Inflated Data, Grayson W. White, Josh K. Yamamoto, Dinan H. Elsyad, Julian F. Schmitt, Niels H. Korsgaard, Jie Hu, George C. Gaines Iii, Tracey S. Frescino, Kelly S. Mcconville

Faculty Journal Articles

Nationwide Forest Inventories (NFIs) collect data on and monitor the trends of forests across the globe. Users of NFI data are increasingly interested in monitoring forest attributes such as biomass at fine geographic and temporal scales, resulting in a need for assessment and development of small area estimation techniques in forest inventory. We implement a small area estimator and parametric bootstrap estimator that account for zero-inflation in biomass data via a two-stage model-based approach and compare the performance to a Horvitz–Thompson estimator, a post-stratified estimator, and to the unit- and area-level empirical best linear unbiased prediction (EBLUP) estimators. We conduct …

Majority Decision Using Top-Performing Neural Networks Models For Improved Credit Risk Prediction, Vincent Dey

College of Graduate Studies: Theses & Dissertations

Credit risk prediction remains both a challenging and high-interest problem due to the inherently unbalanced nature of financial datasets and the continuous drive for higher pre- dictive precision. In this work, I build upon previous advancements in credit risk modeling and introduce an ensemble-based Artificial Neural Network (ANN) architecture designed to enhance classification performance. By leveraging a selective ensemble of decision net- works, this approach not only improves prediction accuracy but also mitigates the chal- lenges posed by imbalanced data distributions. While the primary focus is on credit risk prediction, my analysis demonstrates that the proposed model can be effectively …

Further Results On Learning Quantum Measurement Classes: Quantum Pac Model For Povm Hypothesis Classes, Arka Prabha Das

Electronic Theses & Dissertations (2024 - present)

This thesis investigates the problem of learning from quantum systems, where each example consists of a quantum state paired with a classical outcome. The task centers on choosing an effective measurement rule from a fixed set to enable accurate prediction of the classical outcome from the quantum state. A central focus lies in understanding whether joint measurement strategies that cannot be separated into local operations offer a real benefit in terms of the number of examples needed for successful learning. We examine conditions under which a non-separable measurement within a given hypothesis class achieves strictly better sample complexity bounds compared …

Theoretical Foundations And Applied Performance Of Periodicity-Aware Imputation: Variable Bandpass Block Bootstrap Methods For Incomplete Time Series, Asmaa Ahmad

Electronic Theses & Dissertations (2024 - present)

Time series data are prevalent across a wide range of disciplines, including health surveillance, public policy, and environmental monitoring. In the presence of underlying cyclical patterns, the integrity of time series analysis depends critically on the ability to detect, model, and impute structured missing data without compromising the temporal structure. This dissertation introduces and validates a novel imputation framework that integrates the Variable Bandpass Periodic Block Bootstrap (VBPBB) into multiple imputation procedures, improving the accuracy, robustness, and interpretability of time series models under high rates of missingness and noise. The overarching goal of this dissertation was to develop and evaluate …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Forecasting Equity Betas Using Option-Implied Moments, Ivan Kolesnikov

CMC Senior Theses

Traditional beta estimates are constructed from historical stock‑and‑market returns and therefore adjust only as fast as realized data accrue. This thesis investigates whether the forward‑looking information embedded in equity‑option prices can enhance beta forecasts. Using near‑end‑of‑day quotes for 236 S&P 500 firms between 2007 and 2024, I extract risk‑neutral variance and skewness, construct five alternative beta estimators (historical, option‑implied, and three hybrids), and evaluate them against realized betas over six‑, twelve‑, and twenty‑four‑month windows. Rolling‑OLS beta remains the most accurate benchmark at short horizons, yet option‑implied moments add economically and statistically significant value when systematic exposure is expected to change …

Analyzing Political Sentiment On Micro-Blogging Data: A Lexicon And Machine Learning Approach To The 2024 U.S. Presidential Election, Ava Grey

CMC Senior Theses

This paper explores the trends in sentiment towards U.S. presidential candidates Kamala Harris and Donald Trump through micro-blogging social media text during the five months leading up to the election. Two datasets of varying sizes and origins were used to contextualize and validate analysis findings. The analyses include both a lexicon-based approach and a machine learning predictive method. Common sentiment analysis techniques like term frequency, term frequency inverse, various lexicons, and n-grams were utilized during the lexicon approach. During the modeling, a random forest was utilized in addition to the methods used during the lexicon approach. Results showed that overall …

In Search Of The Rational Voter In The 2020 Presidential Election: Understanding The Impact Of Voter Costs And Benefits On Turnout, Norou Diawara, Tiffany Henley, Samuel L. Brown, Md Iqbal Hossain

Mathematics & Statistics Faculty Publications

The ability to vote is one of the most valuable rights and privileges afforded by the Constitution of the United States to its citizens. For many, voting is not just a civic duty; it is also a choice. Voting is crucial to our democracy, and any changes to it may affect the efficiency of the democratic process. The bigger question is whether voters behave rationally by engaging in a cost-benefit calculus in deciding whether or not to vote. Using data science, this paper will examine the probability of voting and investigate its impact via cost and benefit among other variables …