Physical Sciences and Mathematics Commons^™

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 …

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 …

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 …

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 …

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 …

An Ensemble Approach For Mapping Snow Water Equivalent In Utah, Logan Schneider

All Graduate Theses and Dissertations, Fall 2023 to Present

Mountain snowpack is an important resource for water management planning in Utah. Snow water equivalent (SWE) is the amount of water contained in a snowpack. A few organizations predict SWE throughout the United States but struggle making accurate predictions in mountainous regions. Weather stations provide accurate measurements of SWE but have limited spatial coverage that hinders the ability to make accurate estimates statewide. This thesis examines the accuracy of current models and proposes using local weather measurements to improve upon national level predictions. An R statistical software package named rsnodas implements this process while allowing the public access to a …

Using Gamification To Foster Student Resilience And Motivation To Learn, And Using Games To Teach Significance Testing Concepts In The Statistics Classroom, Todd Partridge

All Graduate Theses and Dissertations, Fall 2023 to Present

Two studies are outlined in this dissertation.

In the first study, elements of Super Mario Bros. videos games were used to change the way college students in a beginners’ statistics course were graded on their work. This was part of an effort to help students remain optimistic in the face of challenging coursework and even failure on assignments and tests. The study shows that the changes made to the grading structure did help students to keep trying and to use the materials given to them by their professor until they achieved their desired grade in the course, and suggests ways …

Using Natural Language Processing To Quantify The Efficacy Of Language Simplification As A Communication Strategy, Brian Nalley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

People with communication disorders often experience difficulties being understood by unfamiliar listeners or in noisy environments. A common strategy for effectively communicating in these scenarios is to use simpler and more predictable language. Despite the prevalence of this strategy, there has been little to no research to date focused on the effectiveness of language simplification as a communication strategy. This study seeks to begin filling that gap by using natural language processing to determine whether speakers with early-stage Parkinson’s disease and age-matched neurotypical speakers are able to successfully simplify their language while still maintaining the original message.

Simplification was measured …

Statistical Graph Quality Analysis Of Utah State University Master Of Science Thesis Reports, Ragan Astle

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Graphical software packages have become increasingly popular in our modern world, but there are concerns within the statistical visualization field about the default settings provided by these packages, which can make it challenging to create good quality graphs that align with standard graph principles. In this thesis, we investigate whether the quality of graphs from Utah State University (USU) Plan A Master of Science (MS) thesis reports from the years 1930 to 2019 was affected by the rise of graphical software packages. We collected all data stored on the USU Digital Commons website since November 2021 to determine the specific …

Stressor: An R Package For Benchmarking Machine Learning Models, Samuel A. Haycock

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many discipline specific researchers need a way to quickly compare the accuracy of their predictive models to other alternatives. However, many of these researchers are not experienced with multiple programming languages. Python has recently been the leader in machine learning functionality, which includes the PyCaret library that allows users to develop high-performing machine learning models with only a few lines of code. The goal of the stressor package is to help users of the R programming language access the advantages of PyCaret without having to learn Python. This allows the user to leverage R’s powerful data analysis workflows, while simultaneously …

An Interval-Valued Random Forests, Paul Gaona Partida

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There is a growing demand for the development of new statistical models and the refinement of established methods to accommodate different data structures. This need arises from the recognition that traditional statistics often assume the value of each observation to be precise, which may not hold true in many real-world scenarios. Factors such as the collection process and technological advancements can introduce imprecision and uncertainty into the data.

For example, consider data collected over a long period of time, where newer measurement tools may offer greater accuracy and provide more information than previous methods. In such cases, it becomes crucial …

Investigating The Effect Of Greediness On The Coordinate Exchange Algorithm For Generating Optimal Experimental Designs, William Thomas Gullion

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Design of Experiments (DoE) is the field of statistics concerned with helping researchers maximize the amount of information they gain from their experiments. Recently, researchers have been turning to optimal experimental designs instead of classical/catalog experimental designs. One of the most popular algorithms used today to generate optimal designs is the Coordinate Exchange (CEXCH) Algorithm. CEXCH is known to be a greedy algorithm, which means it tends to favor immediate, locally best designs instead of globally optimal designs. Previous research demonstrated that this tradeoff was efficacious in that it reduced the cost of a single run of CEXCH and allowed …

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 …

Examining Political Discourse On Online 8kun And Reddit Forums, Braden Mindrum

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A recent example of political violence in the United States was that of the January 6, 2021, Capitol attack in connection with the certification of Joseph R. Biden’s victory over Donald J. Trump in the 2020 US presidential election. This thesis analyzes the events of January 6, 2021, through the lens of social media discourse. This thesis presents a workflow that acquired over 5 million 8kun and Reddit posts from various apolitical and political forums in the three months preceding and following the Capitol attack on January 6, 2021. Techniques from text analysis are then used to group forums according …

Power Approximations For Generalized Linear Mixed Models In R Using Steep Priors On Variance Components, Sydney Geisler

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

When designing an experiment, researchers often want to know how likely they are to detect statistically significant effects in the resulting data, i.e., they want to estimate their statistical power. The probability distribution method is a flexible way to do this, and it is currently implemented in the statistical software package SAS. This method requires a hypothetical data set (showing the magnitude of hypothesized effects) and constant values of variance components, which are critical elements of the statistical models used. The statistical software package R is increasingly popular, but the probability distribution method has not yet been implemented in R, …

Statistical Challenges And Methods For Missing And Imbalanced Data, Rose Adjei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Missing data remains a prevalent issue in every area of research. The impact of missing data, if not carefully handled, can be detrimental to any statistical analysis. Some statistical challenges associated with missing data include, loss of information, reduced statistical power and non-generalizability of findings in a study. It is therefore crucial that researchers pay close and particular attention when dealing with missing data. This multi-paper dissertation provides insight into missing data across different fields of study and addresses some of the above mentioned challenges of missing data through simulation studies and application to real datasets. The first paper of …

Quantum Computing Simulation Of The Hydrogen Molecule System With Rigorous Quantum Circuit Derivations, Yili Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Quantum computing has been an emerging technology in the past few decades. It utilizes the power of programmable quantum devices to perform computation, which can solve complex problems in a feasible time that is impossible with classical computers. Simulating quantum chemical systems using quantum computers is one of the most active research fields in quantum computing. However, due to the novelty of the technology and concept, most materials in the literature are not accessible for newbies in the field and sometimes can cause ambiguity for practitioners due to missing details.

This report provides a rigorous derivation of simulating quantum chemistry …

A Bayesian Hierarchical Approach For Modeling Virtual Species With Realistic Functional Trait Relationships, Sarah Bogen

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Understanding the spatial and temporal dynamics of plant populations has important implications for the fields of ecology and conservation. A rich body of mathematical modeling approaches, including reaction-diffusion equations and integrodifference equations, have been developed to mechanistically model population spread based on species demography and seed dispersal characteristics. However, with over 390,000 plant species on Earth, it is not feasible to collect complete information on all species for the purpose of drawing generalized conclusions. One means of overcoming such a problem is through trait-based modeling, which seeks to represent realistic combinations of organismal traits rather than focusing on individual species. …

An Introduction To Combinatorics Via Cayley's Theorem, Jaylee Willis

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

In this paper, we explore some of the methods that are often used to solve combinatorial problems by proving Cayley’s theorem on trees in multiple ways. The intended audience of this paper is undergraduate and graduate mathematics students with little to no experience in combinatorics. This paper could also be used as a supplementary text for an undergraduate combinatorics course.

Contributions To Random Forest Variable Importance With Applications In R, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major focus in statistics is building and improving computational algorithms that can use data to predict a response. Two fundamental camps of research arise from such a goal. The first camp is researching ways to get more accurate predictions. Many sophisticated methods, collectively known as machine learning methods, have been developed for this very purpose. One such method that is widely used across industry and many other areas of investigation is called Random Forests.

The second camp of research is that of improving the interpretability of machine learning methods. This is worthy of attention when analysts desire to optimize …

Geometry- And Accuracy-Preserving Random Forest Proximities With Applications, Jake S. Rhodes

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Many machine learning algorithms use calculated distances or similarities between data observations to make predictions, cluster similar data, visualize patterns, or generally explore the data. Most distances or similarity measures do not incorporate known data labels and are thus considered unsupervised. Supervised methods for measuring distance exist which incorporate data labels and thereby exaggerate separation between data points of different classes. This approach tends to distort the natural structure of the data. Instead of following similar approaches, we leverage a popular algorithm used for making data-driven predictions, known as random forests, to naturally incorporate data labels into similarity measures known …

Redefining Nba Basketball Positions Through Visualization And Mega-Cluster Analysis, Alexander L. Hedquist

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Basketball players have historically been classified based on one of five positions, namely Point Guards, Shooting Guards, Small Forwards, and Centers. While grouping players into these five categories may provide general descriptions of their perceived role, these standard positions fall short of describing players based on their true abilities and performance. This MS thesis proposes a method to group players of the National Basketball Association (NBA) from the past 20 seasons into more meaningful and specific player positions. We systematically group these players into nine distinct categories, and we draw from a vast array of visualization tools, techniques, and software …

Dynamic System Discovery With Recursive Physics-Informed Neural Networks, Jarrod Mau

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This thesis presents a novel method, recursive Physics informed neural network, to learn the right hand side of differential equations. The neural network takes in data, then trains, and then acts as a proxy for the differential equation which can be used for modeling. We show the theoretical superiority of the recursive approach. We also use computer simulations to demonstrate the proved properties.

Defining Areas Of Interest Using Voronoi And Modified Voronoi Tesselations To Analyze Eye-Tracking Data, Joanna D. Coltrin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Eye tracking is a technology used to track where someone is looking. Eye-tracking technology is often used to study what people focus on when looking at a photo of another person. The eye-tracking technology records points on a photo that a person is looking at. When the photo being looked at shows a person, the points can be categorized by body part such as head, right hand, left hand, and torso. This thesis presents the use of partially circular areas to define the body parts of the person in the photo and therefore categorize the points collected by the eye-tracker. …

Gps-Denied Navigation Using Synthetic Aperture Radar Images And Neural Networks, Teresa White

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Unmanned aerial vehicles (UAV) often rely on GPS for navigation. GPS signals, however, are very low in power and easily jammed or otherwise disrupted. This paper presents a method for determining the navigation errors present at the beginning of a GPS-denied period utilizing data from a synthetic aperture radar (SAR) system. This is accomplished by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are learned and exploited with a convolutional neural network to recover the initial navigational errors, which can be used to recover the true flight trajectory throughout …

Housing Variables And Immigration: An Exploratory And Predictive Data Analysis In New York City, Jhonatan Medri Cobos

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The relationship between housing and immigration has become relevant in the U.S., especially in a highly populated metropolis such as New York City (NYC). Determining whether immigration status affects home ownership percentage, household rent, or housing cost percentage could help understand the quality of life of NYC residents. Graphical exploration, spatial dependence tests, and spatial autoregressive models of housing and immigration variables provide some insights about their relationships. Our exploration takes place at some geographic subareas of NYC.

Our results first indicate that the housing and immigration data reports spatial dependence; values of a geographic subarea are related to values …

A Phenological Model For A Southern Population Of Mountain Pine Beetle, Catherine E. Wangen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) attacks living Pinus trees across a widespread area of western North America, causing significant ecological and economic damage. The ability to make accurate predictions of how MPB populations across this range will respond to temperatures, which affect MPB progress through life stages, is essential. Northern and southern populations of MPB are genetically different in response to temperature, requiring geographic-specific model parameters. There is not currently a predictive model for the southern MPB life cycle, despite concerns that those populations may be more susceptible to increased numbers of generations per year, which would …

Retail Trading And Stock Volatility: The Case Of Robinhood, Cooper Jones

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

We examine the relation between Robinhood usership and stock market volatility. We show that daily fluctuations in Robinhood usership, which is used to proxy retail trading, significantly influence various measures of volatility. These results might suggest that Robinhood users contribute to noise trading as they are generally individuals trading on name recognition, media coverage, popularity, and familiarity of products, rather than on fundamental values. In our empirical approach, we find that the percentage increase in Robinhood usership Granger causes increases in daily stock volatility.

The Effect Of High Elevation Weather Stations On The Usda's Pasture, Rangeland, And Forage Insurance Program, Wyatt Matthew Feuz

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper examines the effect of high elevation weather stations on the rainfall index used by the Pasture, Rangeland, and Forage insurance program. Weather station data for the state of Utah is used to identify high elevation weather stations and their location. Utilizing the corresponding rainfall index data, the effect of the high elevation weather stations is determined. This paper finds when high elevation weather stations begin reporting there is a jump up of 19.01–27.88 percentage points on average in the rainfall index for the corresponding grid locations. This indicates the rainfall index may not accurately represent actual precipitation amounts …