Statistics and Probability Commons^™

Small But Mighty: Examing The Utility Of Microstatistics In Modeling Ice Hockey, Matt Palmer

Senior Honors Theses

As research into hockey analytics continues, an increasing number of metrics are being introduced into the knowledge base of the field, creating a need to determine whether various stats are useful or simply add noise to the discussion. This paper examines microstatistics – manually tracked metrics which go beyond the NHL’s publicly released stats – both through the lens of meta-analytics (which attempt to objectively assess how useful a metric is) and modeling game probabilities. Results show that while there is certainly room for improvement in understanding and use of microstats in modeling, the metrics overall represent an area of …

Bayesian Semi-Mechanistic Dose-Finding Designs For Phase I Oncology Trials, Chao Yang

Dissertations and Theses (Open Access)

Bayesian adaptive designs are getting more popular in research and in practice because they are flexible and efficient in evaluating an experimental drug. In oncology, despite the great advances in novel dose-finding designs, the high failure rates of clinical cancer drug development from phase I to III trials call for further improvements on novel designs, in addition to the need to promote and adopt novel designs in practice. Because anticancer agents often have a narrow therapeutic index, an accurate identification of the maximum tolerated dose (MTD) in a phase I trial is crucial for identifying a tolerable and efficacious dose …

Non-Destructive Imaging Of Phytosulfokine Trafficking In Plants Using Fiber-Optic Fluorescence Microscopy, Bernard Abakah

Electronic Theses and Dissertations

Plants secrete peptide ligands and use receptor signaling to respond to stress and control development. Understanding these phenomena is key to improving plant health and productivity for food, fiber, and energy applications. Phytosulfokine (PSK), a sulfated peptide hormone, regulates plant cell division, growth, and stress tolerance via specific phytosulfokine receptors (PSKRs). This study uses fiber-optic fluorescence microscopy to elucidate trafficking of PSK in live plants. The microscope features two-color optics and an objective lens connected to a 1-m coherent imaging fiber mounted on either a conventional upright microscope body or 5-axis positioning system (X–Y–Z plus pitch and yaw). PSK and …

A Machine Learning Approach To Evaluate The Effect Of Sodium-Glucose Cotransporter-2 Inhibitors On Chronic Kidney Disease In Diabetes Patients, Solomon Eshun

Theses and Dissertations

Chronic kidney disease (CKD) is a significant complication that contributes to diabetes-related mortality in the United States, and there is growing evidence that sodium-glucose cotransporter 2 inhibitors (SGLT2i) can slow its progression. However, observational studies may suffer from confounding by indication, where patient characteristics and disease severity influence the decision to prescribe SGLT2i. This study utilized electronic health records of individuals with diabetes (from TriNetX) to investigate the effectiveness of SGLT2i on CKD progression. The database provided detailed information on patients’ CKD status, demographics, diagnosis, procedures, and medications, along with corresponding dates of diagnosis and prescription. The study comprised of …

Examining Model Complexity's Effects When Predicting Continuous Measures From Ordinal Labels, Mckade S. Thomas

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many real world problems require the prediction of ordinal variables where the values are a set of categories with an ordering to them. However, in many of these cases the categorical nature of the ordinal data is not a desirable outcome. As such, regression models treat ordinal variables as continuous and do not bind their predictions to discrete categories. Prior research has found that these models are capable of learning useful information between the discrete levels of the ordinal labels they are trained on, but complex models may learn ordinal labels too closely, missing the information between levels. In this …

Inference For Multiple Utility In Time-Dependent Choice Pairs Under Copula-Based Models, Sasanka Adikari

Mathematics & Statistics Theses & Dissertations

Models for discrete choice experiments (DCE) are frequently used to analyze consumer choices about products and services. A family of DCE, best-worst scaling experiments, offers more in-depth insights into consumer preferences by eliciting a best and worst choice from a set of options, rather than just a single preference. Traditional approaches often assume that choices are mutually exclusive over time, which may not always be the case. This dissertation proposes a novel model for DCE that takes into account the changing nature of consumer choices over time and the priority constraint of transition probabilities. The model introduces a copula combination …

Jackknife Empirical Likelihood Tests For Equality Of Generalized Lorenz Curves, Anton Butenko

Electronic Theses, Projects, and Dissertations

A Lorenz curve is a graphical representation of the distribution of income or wealth within a population. The generalized Lorenz curve can be created by scaling the values on the vertical axis of a Lorenz curve by the average output of the distribution. In this thesis, we propose two nonparametric methods for testing the equality of two generalized Lorenz curves. Both methods are based on empirical likelihood and utilize a U -statistic. We derive the limiting distribution of the likelihood ratio, which is shown to follow a chi-squared distribution with one degree of freedom. We conduct simulations to compare the …

Distance Correlation Based Feature Selection In Random Forest, Jose Munoz-Lopez

Electronic Theses, Projects, and Dissertations

The Pearson correlation coefficient is a commonly used measure of correlation, but it has limitations as it only measures the linear relationship between two numerical variables. In 2007, Szekely et al. introduced the distance correlation, which measures all types of dependencies between random vectors X and Y in arbitrary dimensions, not just the linear ones. In this thesis, we propose a filter method that utilizes distance correlation as a criterion for feature selection in Random Forest regression. We conduct extensive simulation studies to evaluate its performance compared to existing methods under various data settings, in terms of the prediction mean …

A Generalized Family Of Exponentiated Composite Distributions With Applications To Insurance And Survival Data, Bowen Liu

UNLV Theses, Dissertations, Professional Papers, and Capstones

The concept of composite distributions was proposed in the early 2000s as a good parametric solution to model the data with heavy tails. Since the concept was proposed, it has been widely used in different areas, such as modeling insurance claim size data, predicting the risk measures in insurance data analysis, fitting survival time data, and modeling precipitation data. While a lot of the composite distributions demonstrated great performances in real applications, many commonly used composite distributions such as the inverse gamma-Pareto (IGP) or exponential-Pareto (EP), did not demonstrate great performances when fitting to several particular data sets. In order …

Quantification Of Various Types Of Biases In Large Language Models, Sudhashree Sayenju

Doctor of Data Science and Analytics Dissertations

Natural Language Processing (NLP) systems are included everywhere on the internet from search engines, language translations to more advanced systems like voice assistant and customer service. Since humans are always on the receiving end of NLP technologies, it is very important to analyze whether or not the Large Language Models (LLMs) in use have bias and are therefore unfair. The majority of the research in NLP bias has focused on societal stereotype biases embedded in LLMs. However, our research focuses on all types of biases, namely model class level bias, stereotype bias and domain bias present in LLMs. Model class …

The 2015 Ncaa Cost-Of-Attendance Stipend And Its Effects On Institutional Financial Aid Packages, Sara Greene

Honors Theses

In 2015, the National Collegiate Athletic Association (NCAA) allowed “Cost of Attendance” (COA) stipends to be offered to athletic recruits for Division I schools. These stipends are intended to allow schools to grant aid to student-athletes beyond a full-ride scholarship to cover additional costs imposed on student-athletes. These stipends created an opportunity for the “Autonomy” Power 5 programs to utilize a competitive tactic to try to win over the top recruits. There is evidence that these COA stipends have caused an increase in the estimated cost of attendance reported by the university. This paper examines if the COA stipends have …

On Cox Proportional Hazards Model Performance Under Different Sampling Schemes, Hani Samawi, Lili Yu, Jingjing Yin

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

Cox’s proportional hazards model (PH) is an acceptable model for survival data analysis. This work investigates PH models’ performance under different efficient sampling schemes for analyzing time to event data (survival data). We will compare a modified Extreme, and Double Extreme Ranked Set Sampling (ERSS, and DERSS) schemes with a simple random sampling scheme. Observations are assumed to be selected based on an easy-to-evaluate baseline available variable associated with the survival time. Through intensive simulations, we show that these modified approaches (ERSS and DERSS) provide more powerful testing procedures and more efficient estimates of hazard ratio than those based on …

Time Series Analysis Of Longitudinally Collected Standard Autoperimetry Data In Glaucoma Patients, Carlyn Childress

Honors College Theses

Glaucoma is a group of eye diseases in which damage gradually occurs to the optic nerve, which often leads to partial or complete loss of vision. As the second leading cause of blindness, there is no cure for glaucoma. Early detection and the tracking of its progression is key to managing the effects of glaucoma. Ordinary Least Squares Regression (OLSR), the most commonly used methodology for tracking glaucoma progression, is inappropriate as the longitudinally collected perimetry data from the glaucoma patients appears to be temporally correlated. Time series models, that account for temporal correlation, are better methods to analyze Mean …

Employee Attrition: Analyzing Factors Influencing Job Satisfaction Of Ibm Data Scientists, Graham Nash

Symposium of Student Scholars

Employee attrition is a relevant issue that every business employer must consider when gauging the effectiveness of their employees. Whether or not an employee chooses to leave their job can come from a multitude of factors. As a result, employers need to develop methods in which they can measure attrition by calculating the several qualities of their employees. Factors like their age, years with the company, which department they work in, their level of education, their job role, and even their marital status are all considered by employers to assist in predicting employee attrition. This project will be analyzing a …

Crime In Los Angeles, Cierra Hughley

Symposium of Student Scholars

This study will examine crimes committed in the city of Los Angeles dating back to the year of 2020. The reported data was pulled from the open data of Los Angeles Police Department. The purpose of this study is to show if gender is related to the three primary crimes: property crimes, violent crimes, or other crimes. Doing so will show which crimes were committed by each gender. Even though this study is on gender and crimes committed; it was a hard decision because there were many variables to choose from. However, exploring the relationship between crime and gender was …

Statistical Analysis Of The Relationship Between Protected Bird Species And National Parks, Katherine Harmon

Symposium of Student Scholars

The ecological diversity of Earth is majorly threatened by habitat loss due to the destruction by human intervention. The conservation status of all identified species are classified into nine categories of varying vulnerability as described by the International Union for Conservation of Nature’s Red List. By understanding the vulnerability of specific species, scientists can work to maintain a viable and healthy ecosystem globally by instilling rules and regulations of observed habitats for threatened species. These habitats are identified by surveying potential locations for threatened species and determining the population size at each site. An example of one of these surveys …

Defining Characteristics That Lead To Cost-Efficient Veteran Nba Free Agent Signings, David Mccain

Honors Projects in Mathematics

Throughout the history of the NBA, decisions regarding the signing of free agents have been riddled with complexity. Franchises are tasked with finding out what players will serve as optimal free agent signings prior to seeing them perform within the framework of their team. This study hypothesizes that the adequacy of an NBA free agent signing can be modeled and predicted through the implementation of a machine learning model. The model will learn the necessary information using training and testing data sets that include various player biometrics, game statistics, and financial information. The application of this machine learning model will …

Teaching About The Global Refugee Crisis, Melissa Kafer

Honors Projects

Around the world, there are more than 30 million refugees (UNHCR, 2023) facing language barriers, cultural differences, prejudice, racism, and xenophobia. The number of admitted refugees in 2022 has more than doubled since 2021 (Duffin, 2022), and yet, many Americans do not know or understand the global refugee crisis. There are misconceptions in America that cause lack of empathy, bias, and prejudice towards refugees. Through the creation of four lesson plans, this research project aims to discover Americans’ misunderstandings regarding refugees and teach them about the crisis to remedy the misconceptions. This study includes a literature review detailing appropriate teaching …

Reducing Restaurant Inventory Costs Through Sales Forecasting, Tyler Mason, Chris Schoen, Trevor Gilbert, Jonathan Enriquez

Senior Design Project For Engineers

Family Restaurant is a local restaurant in the greater Atlanta area that serves a variety of dishes that include an assortment of 19 different proteins. Currently, Family Restaurant places protein orders based on business intuition, and tends to over-stock and sometimes under-stock. To minimize inventory costs by reducing over-stocking and preventing under-stocking of proteins, we applied Facebook Prophet (FB Prophet), ARIMA, and XG Boost machine learning models to predict protein demand and then fed these results into a Fixed Time Period inventory model to make an overall order suggestion based on the specified time period. We trained our models on …

Two Sample Statistical Test For Location Parameters, Narinder Kumar, Arun Kumar

Journal of Modern Applied Statistical Methods

A class of distribution-free tests for the homogeneity of location parameters is proposed and compared with different competitors in terms of Pitman asymptotic relative efficiency. A numerical example is provided and a simulation study is made to check the performance of the tests.

Using A Distributive Approach To Model Insurance Loss, Kayla Kippes

Departmental Honors & Graduate Capstone Projects

Insurance loss is an unpredicted event that stands at the forefront of the insurance industry. Loss in insurance represents the costs or expenses incurred due to a claim. An insurance claim is a request for the insurance company to pay for damage caused to an individual’s property. Loss can be measured by how much money (the dollar amount) has been paid out by the insurance company to repair the damage or it can be measured by the number of claims (claim count) made to the insurance company. Insured events include property damage due to fire, theft, flood, a car accident, …

A Pharmacoepidemiological Study Of Myocarditis And Pericarditis Following The First Dose Of Mrna Covid-19 Vaccine In Europe, Joana Tome, Logan Cowan, Isaac Fung

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

This study assessed the myocarditis and pericarditis reporting rate of the first dose of mRNA COVID-19 vaccines in Europe. Myocarditis and pericarditis data pertinent to mRNA COVID19 vaccines (1 January 2021–11 February 2022) from EudraVigilance database were combined with European Centre for Disease Prevention and Control (ECDC)’s vaccination tracker data. The reporting rate was expressed as events (occurring within 28 days of the first dose) per 1 million individuals vaccinated. An observed-to-expected (OE) analysis quantified excess risk for myocarditis or pericarditis following the first mRNA COVID-19 vaccination. The reporting rate of myocarditis per 1 million individuals vaccinated was 17.27 (95% …

Electric Vehicle Uptake: What Factors Are Motivating The Shift For College-Aged And Older Groups?, Jake Cardines

Honors Projects in Mathematics

Electric vehicles (EVs) arguably are the most quickly expanding form of transportation as the world races toward a greener future with advanced technology and reduced reliance on fossil fuels. This study analyzes various expected inputs to motivating consumers of particular age groups to purchase EVs, including examination of how the idea of EV ownership is currently perceived and testing which factors influence it positively and negatively. Data collected from 113 survey respondents serves as the basis for determining the responsiveness of potential future EV owners to variables such as vehicle brand and charging availability, electric range, costs associated with purchase …

The Bellarmine Bee Bed: Organizing A Native Plant Garden Using Feedback From The Local Community, Kate Moran

Undergraduate Theses

Animal pollinators are the cornerstone of healthy ecosystems. Their survival is essential for the persistence of entire food chains: from the flowers they cross-pollinate directly, to the animals who depend on those plants for nutrition. The establishment of pollinator gardens—particularly ones that consist of native plants—is an effective way to enhance their biodiversity, abundance, and well-being.

The main goal of this thesis is to construct a pollinator garden that maximizes the benefits for animal pollinators using feedback from local gardeners. A survey was used to gather information about the popularity and preferences of 40 flowering plants, and after analyzing the …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

Open Data Indicates That Collegedale Could Be A Bluezone, Tristan Deschamps, Alva Johnson

Campus Research Month

A blue zone is an indicator of exceptional health in a community. Adventists have a blue zone community in Loma Linda, but there has been little research into other Adventist populated areas that could be blue zones. Therefore, our goal is to show that open data suggests that a blue zone may exist near Southern Adventist University, specifically in Collegedale. This data has been gathered from different federal sources, including, the CDC, the US Census Bureau, the Tennessee Department of Health, official state records, and federal documents that are available to the public.

Gpu Utilization: Predictive Sarimax Time Series Analysis, Dorothy Dorie Parry

Modeling, Simulation and Visualization Student Capstone Conference

This work explores collecting performance metrics and leveraging the output for prediction on a memory-intensive parallel image classification algorithm - Inception v3 (or "Inception3"). Experimental results were collected by nvidia-smi on a computational node DGX-1, equipped with eight Tesla V100 Graphic Processing Units (GPUs). Time series analysis was performed on the GPU utilization data taken, for multiple runs, of Inception3’s image classification algorithm (see Figure 1). The time series model applied was Seasonal Autoregressive Integrated Moving Average Exogenous (SARIMAX).

The Effectiveness Of Visualization Techniques For Supporting Decision-Making, Cansu Yalim, Holly A. H. Handley

Modeling, Simulation and Visualization Student Capstone Conference

Although visualization is beneficial for evaluating and communicating data, the efficiency of various visualization approaches for different data types is not always evident. This research aims to address this issue by investigating the usefulness of several visualization techniques for various data kinds, including continuous, categorical, and time-series data. The qualitative appraisal of each technique's strengths, weaknesses, and interpretation of the dataset is investigated. The research questions include: which visualization approaches perform best for different data types, and what factors impact their usefulness? The absence of clear directions for both researchers and practitioners on how to identify the most effective visualization …

Statistical Approach To Quantifying Interceptability Of Interaction Scenarios For Testing Autonomous Surface Vessels, Benjamin E. Hargis, Yiannis E. Papelis

Modeling, Simulation and Visualization Student Capstone Conference

This paper presents a probabilistic approach to quantifying interceptability of an interaction scenario designed to test collision avoidance of autonomous navigation algorithms. Interceptability is one of many measures to determine the complexity or difficulty of an interaction scenario. This approach uses a combined probability model of capability and intent to create a predicted position probability map for the system under test. Then, intercept-ability is quantified by determining the overlap between the system under test probability map and the intruder’s capability model. The approach is general; however, a demonstration is provided using kinematic capability models and an odometry-based intent model.

National Residency Matching Program: Looking At The Data Through Linear Regressions, Jacklyn Tellez

Undergraduate Theses

The National Residency Matching Program (NRMP) oversees the process of medical school graduates being matched to a residency program. The NRMP determines both the hospital and residency program for medical students. Prior to matching, both hospital programs and students rank each other. The NRMP uses these lists to determine the matches. Four distinct models using data from hospitals and applicants were used to determine what characteristics lead to a chance of being matched. Each model went through multiple rounds of testing to determine the importance of the different independent variables. In each data set, the dependent variable is either the …