Physical Sciences and Mathematics Commons^™

Introduction To Statistical Thinking, Leslie Bain

ATU Faculty OER Book Reviews

Review of OER Statistics textbook by Benjamin Yakir, available at https://open.umn.edu/opentextbooks/textbooks/introduction-to-statistical-thinking

Recursive Marix Game Analysis: Optimal, Simplified, And Human Strategies In Brave Rats, William A. Medwid

Master's Theses

Brave Rats is a short game with simple rules, yet establishing a comprehensive strategy is very challenging without extensive computation. After explaining the rules, this paper begins by calculating the optimal strategy by recursively solving each turn’s Minimax strategy. It then provides summary statistics about the complex, branching Minimax solution. Next, we examine six other strategy models and evaluate their performance against each other. These models’ flaws highlight the key elements that contribute to the effectiveness of the Minimax strategy and offer insight into simpler strategies that human players could mimic. Finally, we analyze 123 games of human data collected …

The Impact Of Video Assistant Referee (Var) On The English Premier League, Jack Kenyon Brown

Master's Theses

The aim of this study is to examine how the introduction of the Video Assisted Referee (VAR) system influenced the English Premier League (EPL). Since its implementation in the English Premier League in 2019, VAR has been a constant source of debate and controversy. Many studies have been done on the immediate impact of VAR on other elite professional soccer leagues, but the scope of results is very limited and due to be updated. The data for the ensuing analysis consists of 3800 matches played in the English Premier League during the five seasons before (14/15, 15/16, 16/17, 17/18, and …

A Statistical Look Into How Common Soccer Metrics Influence Expected Goal Measures In The Professional Game, Tristan George Rumsey

Undergraduate Honors Thesis Collection

The advent of sports analytics has ignited a fervor across all sporting disciplines, particularly soccer, where clubs are sprinting to harness vast data reserves to elevate team performance, spearhead effective marketing endeavors, and bolster financial gains crucial for club expansion. Much like Billy Beane's transformative "Moneyball" approach, soccer clubs are in pursuit of innovative strategies to transcend financial limitations and achieve triumph. In soccer, where goals are scarce commodities, heightened offensive efficacy becomes imperative. Presently, one metric stands out as pivotal in gauging a team's goal-scoring success: expected goals (xG). This metric quantifies the likelihood of a given shot or …

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 …

Descriptions Of Interglacial Mastodons From Snowmass, Colorado, Connor White

Electronic Theses and Dissertations

The Ziegler Reservoir fossil site (ZRFS) in Colorado contains over 4000 mastodon bones that date from 140,000 to 100,000 years ago. At an elevation of ~2705 meters above sea level, ZRFS represents an alpine ecosystem dated to Marine Isotope Stage (MIS) 5. Formal descriptions of cheek teeth, mandibles, crania, and femora were completed. Statistical analyses of the upper and lower third molars, including a novel measurement of interloph(id) distances, indicate significant differences between ZRFS mastodons and Mammut pacificus, while falling within the ranges for Mammut americanum. This study agrees with the taxonomic assignment of ZRFS mastodons to Mammut …

Using Probability Theory To Calculate The Odds That Either Candidate Wins The 2024 Presidential Election, Andrew Ruggero

Department of Applied Mathematics & Statistics Faculty Publications

In the U.S., where the electoral college is used to determine the votes of an election, calculating the odds of a president winning is not as simple as looking at the total vote percentages. With each state not exactly having a proportionally linear amount of votes per its population, the total percentage doesn’t mean much. As such, in order to calculate these odds, we must look at a variety of winning combinations per each candidate. First, we must take into account that swing states are the only ones that matter. Defined as a 5% difference between the two main candidates, …

A Survey Of The Murray State University Csis Department Of Student And Instructor Attitudes In Relation To Earlier Introduction Of Version Control Systems, Gavin Johnson

Honors College Theses

Over the previous 20 years, the software development industry has overseen an evolution in application of Version Control Systems (VCS) from a Centralized Version Control System (CVCS) format to a Decentralized Version Control Format (DVCS). Examples of the former include Perforce and Subversion whilst the latter of the two include Github and BitBucket. As DVCS models allow software contributors to maintain their respective local repositories of relevant code bases, developers are able to work offline and maintain their work with relative fault tolerance. This contrasts to CVCS models, which require software contributors to be connected online to a main server. …

"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 …

Identifying Rural Health Clinics Within The Transformed Medicaid Statistical Information System (T-Msis) Analytic Files, Katherine Ahrens Mph, Phd, Zachariah Croll, Yvonne Jonk Phd, John Gale Ms, Heidi O'Connor Ms

Rural Health Clinics

Researchers at the Maine Rural Health Research Center describe a methodology for identifying Rural Health Clinic encounters within the Medicaid claims data using Transformed Medicaid Statistical Information System (T-MSIS) Analytic Files.

Background: There is limited information on the extent to which Rural Health Clinics (RHC) provide pediatric and pregnancy-related services to individuals enrolled in state Medicaid/CHIP programs. In part this is because methods to identify RHC encounters within Medicaid claims data are outdated.

Methods: We used a 100% sample of the 2018 Medicaid Demographic and Eligibility and Other Services Transformed Medicaid Statistical Information System (T-MSIS) Analytic Files for 20 states …

Hockey Card Statistics Are Stagnant And Stale, Egan J. Chernoff

Journal of Humanistic Mathematics

The purchase of a coffee at a Canadian institution, Tim Hortons, turned into an informal investigation into hockey card statistics. Turns out, hockey card statistics are stagnant and stale. This was disappointing to see because the game of hockey has changed, the statistics used to keep track of the game have changed. Even the cards have changed. Well, not the back of the cards, which do not well enough paint a statistical picture of the hockey player photographed on the front of the card.

The Limits Of Data Science, David E. Drew

Journal of Humanistic Mathematics

Data science can contribute valuable predictions in diverse fields. But I write to express some concerns and red flags. I suggest that data science is being oversold. This article contains three questions that I believe data science must address as this new discipline matures. Is data science significantly different from statistics? This is a question that has haunted the field since the term first was introduced. By creating algorithms based on current societal decision rules that may be biased, even bigoted, does data science lock in and exacerbate inequality? Scholars have identified a continuum from data to information to knowledge …

Radiofrequency Interference Detection Using Lstmand Statistical Analysis Discriminator, Luke Smith

Masters Theses

"Wireless devices are becoming increasingly pervasive across all aspects of society. Examples of such devices include radios, routers, mobile phones, tablets, and more. As the number of radio frequency (RF) devices continues to rise, so does the amount of interference and noise increase. This is why an efficient approach to interference detection is explored. Most research within this area has been done strictly within the frequency domain as viewing a signal within this domain provides many insights into what makes the signal. This has, however, led to the time domain being underutilized for this area of research.

To explore the …

Defensive Impact Wins: Developing A New Method To Rate Individual Defense In Nba Games, Dylan J. Stiles

Honors Theses and Capstones

With the analytics revolution in sports in the past 20 years, it seems that everything that can be quantified is. In basketball though, trying to break the game down into a set of numbers comes with a unique problem. While we've come up with a good set of advanced numbers to measure offensive efficiency, defense is fundamentally harder to quantify. The game is played five on five, but it has often been popular or convenient to model defense as a set of five one on one games. As defenses became more complex into the 2010s, this methodology became more insignificant. …

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

To Mean Or Not To Mean: An Investigation Of Regression To The Mean, Hunter Ellis

Williams Honors College, Honors Research Projects

Regression to the mean is a statistical phenomenon that can hide important characteristics of what is truly happening in a research study. Caused by statistical randomness, regression to the mean occurs when extreme values, high or low, are followed by less extreme values. To correctly deal with it, one must understand what it is and how to distinguish its effect on conclusions made from the data. This paper provides examples of regression to the mean in both a medical and academic performance study and explains simple identifiers one can observe. Those are then followed up by the introduction of the …

Ensemble Classification: An Analysis Of The Random Forest Model, Jarod Korn

Williams Honors College, Honors Research Projects

The random forest model proposed by Dr. Leo Breiman in 2001 is an ensemble machine learning method for classification prediction and regression. In the following paper, we will conduct an analysis on the random forest model with a focus on how the model works, how it is applied in software, and how it performs on a set of data. To fully understand the model, we will introduce the concept of decision trees, give a summary of the CART model, explain in detail how the random forest model operates, discuss how the model is implemented in software, demonstrate the model by …

Bayesian Analyses For Time-Varying Data And Opinion Dynamics, Torin Quinlivan

Graduate Research Theses & Dissertations

We consider Bayesian analyses for time-varying data from the opinion dynamics in social networks and the processes of sensorimotor learning. Firstly, understanding the underlying opinions of social media users is a difficult process, as they must be understood filtered through the messages sent. To understand how to best estimate the latent opinions, we use a Bayesian approach to estimate various characteristics of the users and the network. We present a model for using Bayesian methods for this problem, along with a simulation study to demonstrate effectiveness. Secondly, incentivization with punishments or rewards may affect human skill learning. To investigate the …

Interpretable Word-Level Sentiment Analysis With Attention-Based Multiple Instance Classification Models, Chenyu Yang

Statistical Science Theses and Dissertations

In this study, our main objective is to tackle the black-box nature of popular machine learning models in sentiment analysis and enhance model interpretability. We aim to gain more insight into the decision-making process of sentiment analysis models, which is often obscure in those complex models. To achieve this goal, we introduce two word-level sentiment analysis models.

The first model is called the attention-based multiple instance classification (AMIC) model. It combines the transparent model structure of multiple instance classification and the self-attention mechanism in deep learning to incorporate the contextual information from documents. As demonstrated by a wine review dataset …

Deep Learning For Microbiome-Based Integrative Modeling And Microbial Biomarkers Identification, Sen Yang

Statistical Science Theses and Dissertations

The human microbiome, comprising trillions of microorganisms, plays a pivotal role in modulating host physiology via molecular and metabolite exchanges. One of the major challenges in this field lies in the effective integration of microbiome and metabolomics data, an achievement that holds the promise of substantially enhancing the precision of disease prediction. However, many datasets prioritize microbiome data while neglecting paired metabolome information. Additionally, the prevalent analytical tools face challenges in effectively merging these intricate datasets, leading to possible misinterpretations and reduced prediction accuracies.

To address these challenges, the first part of this research introduces the Microbiome-based Supervised Contrastive Learning …

Differentiation Of Human, Dog, And Cat Hair Fibers Using Dart Tofms And Machine Learning, Laura Ahumada, Erin R. Mcclure-Price, Chad Kwong, Edgard O. Espinoza, John Santerre

SMU Data Science Review

Hair is found in over 90% of crime scenes and has long been analyzed as trace evidence. However, recent reviews of traditional hair fiber analysis techniques, primarily morphological examination, have cast doubt on its reliability. To address these concerns, this study employed machine learning algorithms, specifically Linear Discriminant Analysis (LDA) and Random Forest, on Direct Analysis in Real Time time-of-flight mass spectra collected from human, cat, and dog hair samples. The objective was to develop a chemistry- and statistics-based classification method for unbiased taxonomic identification of hair. The results of the study showed that LDA and Random Forest were highly …

A Prompt Engineering Approach To Creating Automated Commentary For Microsoft Self-Help Documentation Metric Reports Using Chatgpt, Ryan Herrin, Luke Stodgel, Brian Raffety

SMU Data Science Review

Microsoft collects an immense amount of data from the users of their product-self-help documentation. Employees use this data to identify these self-help articles' performance trends and measure their impact on business Key Performance Indicators (KPIs). Microsoft uses various tools like Power BI and Python to analyze this data. The problem is that their analysis and findings are summarized manually. Therefore, this research will improve upon their current analysis methods by applying the latest prompt engineering practices and the power of ChatGPT's large language models (LLMs). Using VBA code, Microsoft Excel, and the ChatGPT API as an Excel add-in, this research …

Translation Speed Influence On Tropical Cyclone Storm Tide And Surge Generation Along The Gulf Of Mexico Coast, Samantha L. Camarda

LSU Master's Theses

This research examines tropical cyclone translation speed as a factor in storm tide and surge height upon landfall on the United States Gulf Coast. Understanding the effect of translation speed on peak storm tide/surge height is needed to better prepare for and predict future damage from tropical cyclone events. Tropical cyclone data are taken from hourly interpolated best-track HURDAT2 data from 1970–2021. This study uses the HURDAT2 hourly interpolated observation data points (24-hours) pre-landfall to landfall. Translation speed is calculated based on the distance traversed between hourly points. Peak storm tide and storm surge data are taken from SURGEDAT from …

Bayesian Statistical Modeling Of Spatially Resolved Transcriptomics Data, Xi Jiang

Statistical Science Theses and Dissertations

Spatially resolved transcriptomics (SRT) quantifies expression levels at different spatial locations, providing a new and powerful tool to investigate novel biological insights. As experimental technologies enhance both in capacity and efficiency, there arises a growing demand for the development of analytical methodologies.

One question in SRT data analysis is to identify genes whose expressions exhibit spatially correlated patterns, called spatially variable (SV) genes. Most current methods to identify SV genes are built upon the geostatistical model with Gaussian process, which could limit the models' ability to identify complex spatial patterns. In order to overcome this challenge and capture more types …

Reu-Deim Classification Of Hispanic Voters In Hispanic Groups Using Name And Zip Code Data In Palm Beach, Florida, Kamila Soto-Ortiz

Beyond: Undergraduate Research Journal

When it comes to registering to vote, Hispanic voters can only register as “Hispanic” in the “Race/Ethnicity” category, causing difficulties when analyzing voting trends amongst the Hispanic community. Upon the recent idea that not all Hispanic Groups vote the same, the goal is to create a model that can possibly identify a voter’s Hispanic Group with the information provided on the public Florida voter file. This is accomplished using name and zip code data for all voters in Palm Beach, Florida. This paper will explore the model implemented, its findings and limitations. Palm Beach, Florida, is met with low confidence …

Traditional Vs Machine Learning Approaches: A Comparison Of Time Series Modeling Methods, Miguel E. Bonilla Jr., Jason Mcdonald, Tamas Toth, Bivin Sadler

SMU Data Science Review

In recent years, various new Machine Learning and Deep Learning algorithms have been introduced, claiming to offer better performance than traditional statistical approaches when forecasting time series. Studies seeking evidence to support the usage of ML/DL over statistical approaches have been limited to comparing the forecasting performance of univariate, linear time series data. This research compares the performance of traditional statistical-based and ML/DL methods for forecasting multivariate and nonlinear time series.

Statistical Precision Of A Replicated Farm Grazing Trial Versus Replicated Paddock Trials, K. P. Vogel, L. E. Moser, D. E. Bauer

IGC Proceedings (1977-2023)

The experimental unit for animal average daily gain (ADG) and gain/ha in grazing trials is the paddock. Grazing trials on research stations often are conducted using small paddocks because animal and land costs restrict the number of treatments, replicates, and animals per paddock. Land and animal restrictions can be reduced by conducting trials on farms using animals provided by cooperating farmers. Farmers typically want only a single replicate on their farms and as result, virtually all on-farm trials in the USA and elsewhere have been un-replicated demonstration trials from which estimates of experimental error cannot be obtained. Farms can be …

Sentiment Analysis Before And During The Covid-19 Pandemic, Emily Musgrove

Mathematics Summer Fellows

This study examines the change in connotative language use before and during the Covid-19 pandemic. By analyzing news articles from several major US newspapers, we found that there is a statistically significant correlation between the sentiment of the text and the publication period. Specifically, we document a large, systematic, and statistically significant decline in the overall sentiment of articles published in major news outlets. While our results do not directly gauge the sentiment of the population, our findings have important implications regarding the social responsibility of journalists and media outlets especially in times of crisis.

Optimal Experimental Planning Of Reliability Experiments Based On Coherent Systems, Yang Yu

Statistical Science Theses and Dissertations

In industrial engineering and manufacturing, assessing the reliability of a product or system is an important topic. Life-testing and reliability experiments are commonly used reliability assessment methods to gain sound knowledge about product or system lifetime distributions. Usually, a sample of items of interest is subjected to stresses and environmental conditions that characterize the normal operating conditions. During the life-test, successive times to failure are recorded and lifetime data are collected. Life-testing is useful in many industrial environments, including the automobile, materials, telecommunications, and electronics industries.

There are different kinds of life-testing experiments that can be applied for different purposes. …

A Comparison Of Confidence Intervals In State Space Models, Jinyu Du

Statistical Science Theses and Dissertations

This thesis develops general procedures for constructing confidence intervals (CIs) of the error disturbance parameters (standard deviations) and transformations of the error disturbance parameters in time-invariant state space models (ssm). With only a set of observations, estimating individual error disturbance parameters accurately in the presence of other unknown parameters in ssm is a very challenging problem. We attempted to construct four different types of confidence intervals, Wald, likelihood ratio, score, and higher-order asymptotic intervals for both the simple local level model and the general time-invariant state space models (ssm). We show that for a simple local level model, both the …