Statistics and Probability Commons^™

Human Capital And Lifetime Income Gains Of Scaling-Up Small-Quantity Lipid Nutrient Supplements Among Children Under 2 Years: A Modelling Analysis, Nandita Perumal Phd, Goodrarz Danaei, Günther Fink, Mark Lambiris, Christopher R. Sudfeld

Faculty Publications

Undernutrition in early childhood is associated with adverse health and developmental outcomes later in life and remains a persistent global public health problem. Providing small-quantity lipid nutrient supplements (SQ-LNS) to children aged 6-24 months improves child growth and neurodevelopmental outcomes, but the potential long-term benefits to human capital have not been previously estimated. We estimated the potential returns to schooling and lifetime income attributable to increasing coverage of SQ-LNS for children < 2 years of age from 0% to 50% or 90% per five-year birth cohort in five countries (Bangladesh, Burkina Faso, Ethiopia, Pakistan, and Uganda) with a high burden of undernutrition. Random-effects meta-analyses were used to estimate the effect of SQ-LNS on child development using evidence from randomized controlled trials, and to estimate the returns to lifetime income as a function of change in development based on a de novo meta-analysis of observational economic studies. Gains in school years attributable to scaling-up SQ-LNS to 90% coverage ranged from 0.14 million school years (95% uncertainty interval [UI]: 0.064, …

Leveraging Benford’S Law And Machine Learning For Financial Fraud Detection, Benjamin R. Fu

Cybersecurity Undergraduate Research Showcase

Financial fraud, particularly credit card fraud, continues to pose substantial challenges to financial institutions due to its increasing frequency and impact on consumer trust. While traditional rule-based methods have provided foundational defenses, their limitations in scalability and adaptability have accelerated the adoption of machine learning (ML) techniques. Concurrently, Benford’s Law—a statistical principle often used in forensic accounting—has demonstrated efficacy in detecting anomalies within naturally occurring numerical datasets. This study explores a hybrid fraud detection approach that integrates Benford’s Law with supervised machine learning algorithms, including Logistic Regression, Random Forest, and k-Nearest Neighbors. Using the publicly available European credit card fraud …

Existence Of Bounded Asymptotic Solutions Of Autonomous Differential Equations, Minh Van Nguyen Dr., Vu Trong Luong, William Barker, Duchuy Nguyen

Faculty Scholarship

We study the existence of bounded asymptotic mild solutions to evolution equations of the form u′(t)=Au(t)+f(t),t≥0in a Banach space X, where Agenerates an (analytic) C0-semigroup and fis bounded. We fifind spectral conditions on Aand ffor the existence and uniqueness of asymptotic mild solutions with the same as that of f. In the resonance case, a sufficient condition of Massera type theorem is found for the existence of bounded solutions with the same profifile as f. The obtained results are stated in terms of spectral properties of Aand f, and they are analogs of classical results of Katznelson-Tzafriri and Massera for …

Ahr Activation At The Air-Blood Barrier Alters Systemic Microrna Release After Inhalation Of Particulate Matter Containing Environmentally Persistent Free Radicals, Ankit Aryal, Ashlyn C. Harmon, Alexandra Noël, Qingzhao Yu, Kurt J. Varner, Tammy R. Dugas

School of Public Health Faculty Publications

Particulate matter containing environmentally persistent free radicals (EPFRs) is formed when organic pollutants are incompletely burned and adsorb to the surface of particles containing redox-active metals. Our prior studies showed that in mice, EPFR inhalation impaired vascular relaxation in a dose- and endothelium-dependent manner. We also observed that activation of the aryl hydrocarbon receptor (AhR) in the alveolar type-II (AT-II) cells that form the air-blood interface stimulates the release of systemic factors that promote endothelial dysfunction in vessels peripheral to the lung. AhR is a recognized regulator of microRNA (miRNA) biogenesis, and miRNA control diverse signaling pathways. We thus hypothesized …

A Machine-Learning Tool-Supported Methodology For Nonprofit Donor Analysis, Corbin Weiss

Campus Research Month

We developed a machine-learning tool-supported methodology for modeling the nonprofit donor relationship. This approach was demonstrated in the case of a US-based nonprofit. Conclusions were drawn from this example and tool-support provided for use by other nonprofits.

Prenatal Exposure To Pm2.5 Concentration And Risk Of Preterm Birth In New Mexico; A Seasonal Pattern And Spatio-Temporal Modeling., Onyedikachi J. Okeke

Mathematics & Statistics ETDs

This study investigates the association between prenatal PM2.5 exposure and preterm birth risk in New Mexico (2014–2021). Using descriptive statistics, time series models, and spatial analyses, findings show an average preterm birth rate of 14.87 per 1,000 live births, with moderate correlation (r = 0.727) between PM2.5 levels and very preterm births. While traditional models revealed no significant global effect, spatial methods such as Geographically Weighted Regression (GWR) and Multiscale GWR uncovered strong spatial heterogeneity. PM2.5 effects varied by county (coefficients: -0.00154 to 0.00150), with clustering evident in 2018–2019 (Moran’s I = 0.155–0.174). Results highlight the limitations of global models …

Predicting Capture And Survival Probabilities Of The Arizona Tiger Salamander: A Comparison Of Capture-Recapture Models, Brittney Nelson

Scholars Week

Capture-recapture models are essential tools for estimating population dynamics in ecological studies. A fundamental component of these models is the capture history matrix, which records individual detection over time and serves as the basis for estimating survival and capture probabilities. This presentation explores three statistical approaches to these estimations: the Cormack-Jolly-Seber (CJS) model, the Hidden Markov Model (HMM) for CJS, and the Bayesian CJS model. The CJS model provides a likelihood-based framework for estimation, and the HMM CJS incorporates latent states into the model to account for uncertainty in detection. The Bayesian CJS extends this same analysis by integrating prior …

Evaluating The Performance Of Bayesian Removal Models For Estimating Population Density And Detecting Trends With Variable Detection Probability, David R. Stewart

Mathematics & Statistics ETDs

Removal models have long been used to estimate population abundance by progressively capturing and removing individuals from a closed population. These models provide a valuable tool for ecological monitoring, but their accuracy depends heavily on assumptions about detection probability, which may decline over successive sampling passes. Traditional removal models assume constant detection probabilities, an assumption that is often violated in real-world applications. This thesis aims to advance hierarchical Bayesian models by accounting for variable detection probabilities, improving the reliability of abundance estimates and trend detection. By integrating simulation-based analyses with empirical data from Lahontan Cutthroat Trout (Oncorhynchus clarkia henshawi …

Robust Multifidelity Operator Learning For Partial Differential Equations, Jacob Hauck, Yanzhi Zhang

Miners Solving for Tomorrow Research Conference

No abstract provided.

Statistical Programming Package For Simplified Data Exploration, Liam Raymon, Jennifer Schon

Celebration of Research

Simple linear regression can be very helpful for exploring a dataset through identifying variable relationships and the percentage of variance in the dependent variable explained by the model. The project showcases a coding package for the statistical programming language R that I have created to provide a streamlined approach to exploring data through linear regression. Packages serve as extensions of coding languages to add features or functions. This package automates simple linear regression and outputs key values for data exploration such as p value, R^2, and independent variable coefficients in an organized and concise manner. In addition to regression, this …

Opioid Vs. Money Choice Preference Patterns In Regular Heroin Users, Amolak S. Jhand, Mark Greenwald

Medical Student Research Symposium

About two-thirds of people treated for opioid use disorder (OUD) return to opioid use within the first-year post-treatment, and about 10% report use while on agonist therapy. Understanding determinants of opioid-seeking is vital to reducing recurrence and its risks. We assessed individual differences in effortful choices between opioid and money amounts, modeling real-world choices.

Our lab conducted studies in which regular heroin-users were stabilized on buprenorphine to suppress withdrawal. Within experimental sessions, the participant could choose repeatedly across 12 trials between units of hydromorphone (HYD, 1 or 2 mg IM) vs. money ($2 or $4); HYD and money amounts differed …

Unraveling The Impact Of Curricular Complexity On Graduation Time: A Causal Analysis In Higher Education, Ameer Slim

Mathematics & Statistics ETDs

This study examines the causal relationship between program complexity and graduation time at UNM. While program complexity is recognized as a factor influencing student outcomes, its precise impact on graduation timelines remains underexplored. Using comprehensive cohort data, this study employs causal inference methods, including generalized propensity scores, to estimate the effect of complexity on time-to-degree. Findings reveal that higher program complexity extends graduation timelines, even after controlling for demographics and academic preparedness. Socioeconomic factors also play a role. Specifically, programs with more Pell Grant recipients and lower median high school GPAs tend to have lower complexity levels. These results provide …

Quarterback Statistics Vs. Season Success, Brendan Woods

Mathematics Senior Capstone Papers

The purpose of this research is to determine which quarterback statistic most significantly impacts team success in the National Football League. By analyzing data from quarterbacks with at least 100 pass attempts per season from 2006 to 2023, we examine the relationship between quarterback rating, passer rating, completion percentage, and TD-INT ratio with end-of-season power rankings. We ran the data through multiple linear regression models to identify which statistic has the strongest correlation with team performance. Our model considers variations across different seasons and accounts for statistical trends over time. With over 17 seasons of data analyzed, further exploration could …

The Effect Of Internal Consistency On Ncaa Women’S Gymnastics Scores, Jordan Williams

Mathematics Senior Capstone Papers

The aim of my research is to examine internal consistency in relation to the validity of scores in NCAA Women’s Gymnastics. This study focuses on scores from the now infamous 2024 Tennessee Collegiate Classic. Patterns from several different deviations and correlation coefficients are analyzed, and a “gold standard” score to test against is created. This allows me to identify several patterns in results that could signify invalid scores.

Faculty Diversity And Minority Enrollment In Advanced Stem Courses: A Case Study At Neville High School, Anaya Cormier

Mathematics Senior Capstone Papers

This study investigates the correlation between the diversity of STEM faculty and the enrollment rates of minority students in honors, Advanced Placement (AP), and dual enrollment STEM courses at Neville High School. Recognizing the long-standing underrepresented minority students in advanced STEM education, this research explores whether a more diverse faculty positively influences student participation in these courses. Using a quantitative correlational design, data on faculty demographics and student enrollment patterns were analyzed through descriptive statistics and chi-square tests of independence. The results are expected to provide information on the role of faculty diversity in fostering equitable academic opportunities. The findings …

An Analysis Of The Alaskan Salmon Harvest, Carson Allen

Mathematics Senior Capstone Papers

The objective of this paper is to analyze the annual Alaskan salmon harvest and the variables that effect the harvest differently each year. Every year, thousands of workers’ livelihoods depend on the annual salmon harvest to provide for themselves and their families. This paper takes this reality and aims to use data gathered from previous fishing seasons to understand what variables affect the salmon population. To analyze the salmon harvest, multiple linear regression will be used over a 41 year period with variables including water temperature, air temperature, yearly harvest, and species of salmon. By modeling these and other variables, …

Some New Hardy-Type Inequalities With Negative Parameters On Time Scales, Martin Bohner, Irena Jadlovská, Ahmed I. Saied

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we present new Hardy-type inequalities with negative parameters on a time scale T. The adopted approach draws upon the use of a reversed Hölder dynamic inequality, a chain rule, and the integration by parts rule on time scales. In the continuous case, our results contain integral inequalities due to Benaissa and Budak, while in the discrete case, the obtained inequalities are essentially new. Additionally, we demonstrate the applicability of our results in the quantum case.

Irreversible K-Threshold Number Ck(G) And Saturation Probability P[G] For Corona Product And Double Corona Product Graphs, Eric J. Moon, Soumya Bhoumik, Paul Flesher

SACAD: Scholarly Activities

We discuss the Irreversible k-conversion process for graphs, where a vertex becomes saturated and remains saturated indefinitely if at least k of its neighbors are saturated. We investigate sets S₀, which when initially saturated, lead to complete graph saturation. We are interested in the minimum |S₀| = C_k(G), called the k-threshold number. We consider the construction of the Corona Product Graphs (of C_n and K_p). Additionally, we extend our analysis by defining and exploring Double Corona Product Graphs (of C_n and K_p). Then we incorporate …

Repositioning The Game: Traditional Positions Vs Tracking-Based Archetypes In Nba Performance Models, Jacob Floyd

Senior Theses

Driven by the rise of advanced analytics and player tracking technologies, the NBA has transitioned away from traditional positional roles and toward more fluid player archetypes. This investigation uses principal component analysis and k-means clustering to group players based on season-long tracking data, creating new pseudo-positions that more accurately reflect modern playing styles. Predictive models were then built using both the classic position system and the newly generated clusters to forecast player scoring performance. Across every model comparison, both in terms of fit and predictive accuracy, the cluster-based system significantly outperformed the traditional position-based model. These results reinforce the idea …

Simulation Research On Financial Competitive Intelligence Early Warning Mechanism Of New Ventures Based On Big Data Thinking, Keping Wang, Jingyi Zhou, Yao Che, Zhen Qiao

Journal of Scientific Information Research

[Purpose/significance]Financial competitive intelligence is a core element in promoting the stable development of new ventures. Based on big data thinking, exploring the construction process and simulation effects of financial competitive intelligence warning mechanisms for new ventures is of great significance for improving their competitiveness and promoting healthy development. [Method/process]The article takes startups as the research object, constructs a financial competitive intelligence early warning mechanism for startups based on big data thinking, and uses system dynamics methods to construct causal relationship diagrams and system flow diagrams, and simulates them using Vensim PLE software. [Result/conclusion]The system dynamics model constructed in the article …