Statistics and Probability Commons^™

Time Scale Separation In Life-Long Ovarian Follicles Population Dynamics Model, Romain Yvinec, Frédérique Clément, Guillaume Ballif

Biology and Medicine Through Mathematics Conference

No abstract provided.

Multi-Type Branching Processes In Time-Varying Environments, Arash Jamshidpey

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Human Temporal Eeg Responses To Vr Visual Stimuli, Richard R. Foster, Connor Delaney, Dean J. Krusienski, Cheng Ly

Biology and Medicine Through Mathematics Conference

No abstract provided.

Calculations From On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

Mathematics and Statistics Student Research and Class Projects

In the field of nonlinear waves, particular interest is given to periodic traveling-wave solutions of nonlinear, dispersive wave equations. This thesis aims to determine the existence of periodic traveling-wave solutions for several systems of water wave equations. These systems are the Schr¨odinger KdV-KdV, Schr¨odinger BBM-BBM, Schr¨odinger KdV-BBM, and Schr¨odinger BBM-KdV systems, and the abcd-system. In particular, it is shown that periodic traveling-wave solutions exist and are explicitly given in terms of cnoidal, the Jacobi elliptic function. Certain solitary-wave solutions are also established as a limiting case of the periodic traveling-wave solutions, that is, as the elliptic modulus approaches one.

Factors Predictive Of The Development Of Surgical Site Infection In Thyroidectomy, A Replication Study Of Myssiorek (2018), Kaitlyn M. Kenig

Capstone Experience

The original study aimed to show that thyroidectomy does not result in surgical site infection (SSI) in most cases, and thus routine prescription of antibiotics is not necessary. The study looked to see what risk factors could predict the incidence of SSI. This would highlight those individuals who were at most risk of developing SSI, and then antibiotics would only be prescribed to these individuals instead of all or most individuals who undergo thyroidectomy.

This study used NSQIP data to look at incidence of SSI and look for risk factors that may be predictive of SSI. Only surgeries that were …

Using The History Of Statistics To Teach Introductory Statistics, Melissa Hansen

All Graduate Reports and Creative Projects, Fall 2023 to Present

While often taught in high school and required as part of a college degree, statistics classes are sometimes viewed by students as an obstacle rather than a support for their overall goals. One way to increase student engagement in a statistics course is to use the history of statistics. Within the literature review, the advantages to using the history of statistics are discussed as well as the more extensive research on using the history of mathematics in mathematics courses. Included are instructional strategies for using the context around the development of mathematical ideas in math classrooms which can be extended …

High-Dimensional Mediation Analysis Of Multi-Omics Data, Sunyi Chi

Dissertations & Theses (Open Access)

Environmental exposures such as cigarette smoking influence health outcomes through intermediate molecular phenotypes, such as the methylome, transcriptome, and metabolome. Mediation analysis is a useful tool for investigating the role of potentially high-dimensional intermediate phenotypes in the relationship between environmental exposures and health outcomes. Rapid development of high-throughput technologies have made mediation analysis of multi-omics data critical to gain groundbreaking insights into the biological mechanisms underlying the disease etiology. This dissertation aims to develop mediation analysis methods that utilize the enormous amount of multi-omics data in assessing mechanisms of disease etiology. It contains three projects where I propose advanced mediation …

Code For Care: Hypertension Prediction In Women Aged 18-39 Years, Kruti Sheth

Electronic Theses, Projects, and Dissertations

The longstanding prevalence of hypertension, often undiagnosed, poses significant risks of severe chronic and cardiovascular complications if left untreated. This study investigated the causes and underlying risks of hypertension in females aged between 18-39 years. The research questions were: (Q1.) What factors affect the occurrence of hypertension in females aged 18-39 years? (Q2.) What machine learning algorithms are suited for effectively predicting hypertension? (Q3.) How can SHAP values be leveraged to analyze the factors from model outputs? The findings are: (Q1.) Performing Feature selection using binary classification Logistic regression algorithm reveals an array of 30 most influential factors at an …

Exploring Application Of The Coordinate Exchange To Generate Optimal Designs Robust To Data Loss, Asher Hanson

All Graduate Theses and Dissertations, Fall 2023 to Present

The primary objective of this study is to evaluate the efficacy of the coordinate exchange (CEXCH) algorithm in the generation of robust optimal designs. The assessment involves a comparative analysis, wherein designs produced by the Point Exchange (PEXCH) Algorithm are employed as benchmarks for evaluating the efficiency of CEXCH designs. Three modified criteria, selected from the traditional alphabet criteria pool, are utilized to score each algorithm. To enhance the reliability of the comparative analysis, multiple rounds of validation are conducted, focusing on visual assessments, design scores, and criteria efficiencies. The findings from each round of validation contribute to a comprehensive …

The Quantitative Analysis And Visualization Of Nfl Passing Routes, Sandeep Chitturi

Computer Science and Computer Engineering Undergraduate Honors Theses

The strategic planning of offensive passing plays in the NFL incorporates numerous variables, including defensive coverages, player positioning, historical data, etc. This project develops an application using an analytical framework and an interactive model to simulate and visualize an NFL offense's passing strategy under varying conditions. Using R-programming and data management, the model dynamically represents potential passing routes in response to different defensive schemes. The system architecture integrates data from historical NFL league years to generate quantified route scores through designed mathematical equations. This allows for the prediction of potential passing routes for offensive skill players in response to the …

Comparing North American Professional Sports League Season Formats Using Monte Carlo Simulation, Lathan Gregg

Industrial Engineering Undergraduate Honors Theses

Each NFL, NBA, and MLB season consists of a regular season, in which teams play a set number of scheduled games and a playoff, in which qualifying teams compete for a championship. At the conclusion of each season, teams are ranked based on their performance throughout the season. This study aims to investigate the ability of each league's season format to accurately rank teams using Monte Carlo simulation. Matches between two teams are simulated by using the team’s assigned strength ranks to calculate a winning probability for each team. The winning probabilities are simulated with different skill values, dictating how …

Information Based Approach For Detecting Change Points In Inverse Gaussian Model With Applications, Alexis Anne Wallace

Electronic Theses, Projects, and Dissertations

Change point analysis is a method used to estimate the time point at which a change in the mean or variance of data occurs. It is widely used as changes appear in various datasets such as the stock market, temperature, and quality control, allowing statisticians to take appropriate measures to mitigate financial losses, operational disruptions, or other adverse impacts. In this thesis, we develop a change point detection procedure in the Inverse Gaussian (IG) model using the Modified Information Criterion (MIC). The IG distribution, originating as the distribution of the first passage time of Brownian motion with positive drift, offers …

An Improved Bayesian Pick-The-Winner (Ibpw) Design For Randomized Phase Ii Clinical Trials, Wanni Lei, Maosen Peng, Xi K. Zhou

COBRA Preprint Series

Phase II clinical trials play a pivotal role in drug development by screening a large number of drug candidates to identify those with promising preliminary efficacy for phase III testing. Trial designs that enable efficient decision-making with small sample sizes and early futility stopping while controlling for type I and II errors in hypothesis testing, such as Simon’s two-stage design, are preferred. Randomized multi-arm trials are increasingly used in phase II settings to overcome the limitations associated with using historical controls as the reference. However, how to effectively balance efficiency and accurate decision-making continues to be an important research topic. …

Exploring Optimal Design Of Experiments For Random Effects Models, Ryan C. Bushman

All Graduate Theses and Dissertations, Fall 2023 to Present

The majority of research in the field of optimal design of experiments has focused on producing designs for fixed effects models. The purpose of this thesis is to explore how the optimal design framework applies to nested random effects models. The object that is being optimized is the model information matrix. We explore the full derivation of the random effects information matrix to highlight the complexity of the problem and show how the optimization is a function of the model's parameters. In conjunction with this research, the ODVC (Optimal Design for Variance Components) package was built to provide tools that …

Assessing Extant Methods For Generating G-Optimal Designs And A Novel Methodology To Compute The G-Score Of A Candidate Design, Hyrum John Hansen

All Graduate Theses and Dissertations, Fall 2023 to Present

Experimental designs are used by scientists to allocate treatments such that statistical inference is appropriate. Most traditional experimental designs have mathematical properties that make them desirable under certain conditions. Optimal experimental designs are those where the researcher can exercise total control over the treatment levels to maximize a chosen mathematical property. As is common in literature, the experimental design is represented as a matrix where each column represents a variable, and each row represents a trial. We define a function that takes as input the design matrix and outputs its score. We then algorithmically adjust each entry until a design …

On The Existence Of Periodic Traveling-Wave Solutions To Certain Systems Of Nonlinear, Dispersive Wave Equations, Jacob Daniels

All Graduate Theses and Dissertations, Fall 2023 to Present

A variety of physical phenomena can be modeled by systems of nonlinear, dispersive wave equations. Such examples include the propagation of a wave through a canal, deep ocean waves with small amplitude and long wavelength, and even the propagation of long-crested waves on the surface of lakes. An important task in the study of water wave equations is to determine whether a solution exists. This thesis aims to determine whether there exists solutions that both travel at a constant speed and are periodic for several systems of water wave equations. The work done in this thesis contributes to the subfields …

Ianova: Multi-Sample Means Comparisons For Imprecise Interval Data, Zachary Rios

All Graduate Theses and Dissertations, Fall 2023 to Present

In recent years, interval data has become an increasingly popular tool to solve modern data problems. Intervals are now often used for dimensionality reduction, data aggregation, privacy censorship, and quantifying awareness of various uncertainties. Among many statistical methods that are being studied and developed for interval data, the significance test is particularly of importance due to its fundamental value both in theory and practice. The difficulty in developing such tests mainly lies in the fact that the concept of normality does not extend naturally to interval data (due the range of an interval being necessarily non-negative), causing the exact tests …

A Comprehensive Uncertainty Quantification Methodology For Metrology Calibration And Method Comparison Problems Via Numeric Solutions To Maximum Likelihood Estimation And Parametric Bootstrapping, Aloka B. S. N. Dayarathne

All Graduate Theses and Dissertations, Fall 2023 to Present

In metrology, the science of measurements, straight line calibration models are frequently employed. These models help understand the instrumental response to an analyte, whose chemical constituents are unknown, and predict the analyte’s concentration in a sample. Techniques such as ordinary least squares and generalized least squares are commonly used to fit these calibration curves. However, these methods may yield biased estimates of slope and intercept when the calibrant, substance used to calibrate an analytical procedure with known chemical constituents (x-values), carries uncertainty. To address this, Ripley and Thompson (1987) proposed functional relationship estimation by maximum likelihood (FREML), which considers uncertainties …

A Novel Correction For The Multivariate Ljung-Box Test, Minhao Huang

Computational and Data Sciences (PhD) Dissertations

This research introduces an analytical improvement to the Multivariate Ljung-Box test that addresses significant deviations of the original test from the nominal Type I error rates under almost all scenarios. Prior attempts to mitigate this issue have been directed at modification of the test statistics or correction of the test distribution to achieve precise results in finite samples. In previous studies, focused on designing corrections to the univariate Ljung-Box, a method that specifically adjusts the test rejection region has been the most successful of attaining the best Type I error rates. We adopt the same approach for the more complex, …

"Who Wrote The Epistle, God Only Knows": A Statistical Authorial Analysis Of Hebrews In Comparison With Pauline And Lukan Literature, Benjamin J. Erickson

Senior Honors Theses

The authorship of Hebrews has been a point of contention for scholars for the past two millennia. While the epistle is traditionally attributed to Paul, many scholars assert that it carries thematic, structural, and stylistic differences from the remainder of his extant epistles; therefore, many other possible authors have been proposed. Of these, only Luke has other New Testament writings. Therefore, this project conducts a statistical comparison of Hebrews to the Pauline and Lukan corpora using stylometric authorial analysis methods. This analysis demonstrates that Hebrews is stylistically closer to Lukan literature than Pauline (but not to a significant degree), and …