Statistics and Probability Commons^™

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.

An Analysis Of Lyrical Repetition And Popularity In Popular Music Genres, Josh White

Undergraduate Honors Capstone Projects

This paper examines the correlation between repetitiveness and popularity in the genres of Christian, Country, EDM, Hip-Hop, Latin, Pop, R&B, and Rock. Repetitiveness is defined by the frequency of repeated words in lyrics, and the average number of streams per day defines popularity. This analysis also acknowledges the "popularity" metric provided by Spotify in calculating the correlation. To calculate this correlation, I wrote a program that accesses the Spotify and Genius APIs to gather metadata related to 76,069 songs from 1,246 artists, including data on repetitiveness, tempo, duration, and Spotify's audio metrics of "danceability," "energy," "speechiness," "acousticness," and "instrumentalness." I …

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 …

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 …

Evaluating Taxonomic Approaches: A Comparative Study Of Educational Frameworks Applied To Mathematics Assessments, Lily Roth

Undergraduate Honors Capstone Projects

The design of effective assessments and reporting of a student’s achievement on learning objectives are often overlooked, leaving educational stakeholders lacking the ability to create meaningful evaluations. To assist in creating substantial mathematics assessments this work seeks to answer the following research questions: ‘How can educational taxonomies be utilized to improve the design of mathematics assessments’? and ‘What are the strengths and weaknesses of applying different taxonomies onto mathematics assessments?’. The purpose of this study is to (1) develop a practical design instrument for easier identification and categorization of assessment questions within each educational taxonomy structure and (2) evaluate the …

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 …

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 …

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 …

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 …

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 …

Towards Fast, Realistic Gas Plume Simulation For Lwir Hyperspectral Images To Improve Deep Learning Identification Models, Scout Jarman

Student Research Symposium

• Longwave infrared (LWIR) hyperspectral images (HSI) are taken from airborne platforms and can be used to find gas plumes.
• Detection and identification of gas plumes has applications in environmental monitoring, disaster response, and national security
• Deep learning can be used to identify gases from a large library of materials,  but can be difficult to apply in practice

Anomaly Detection On Small Wind Turbine Blades Using Deep Learning Algorithms, Bridger Altice, Edwin Nazario, Mason Davis, Mohammad Shekaramiz, Todd K. Moon, Mohammad A. S. Masoum

Electrical and Computer Engineering Faculty Publications

Wind turbine blade maintenance is expensive, dangerous, time-consuming, and prone to misdiagnosis. A potential solution to aid preventative maintenance is using deep learning and drones for inspection and early fault detection. In this research, five base deep learning architectures are investigated for anomaly detection on wind turbine blades, including Xception, Resnet-50, AlexNet, and VGG-19, along with a custom convolutional neural network. For further analysis, transfer learning approaches were also proposed and developed, utilizing these architectures as the feature extraction layers. In order to investigate model performance, a new dataset containing 6000 RGB images was created, making use of indoor and …

Teaching Reproducibility To First Year College Students: Reflections From An Introductory Data Science Course, Brennan L. Bean

Journal on Empowering Teaching Excellence

Access the online Pressbooks version of this article here.

Modern technology threatens traditional modes of classroom assessment by providing students with automated ways to write essays and take exams. At the same time, modern technology continues to expand the accessibility of computational tools that promise to increase the potential scope and quality of class projects. This paper presents a case study where students are asked to complete a “reproducible” final project in an introductory data science course using the R programming language. A reproducible project is one where an instructor can easily regenerate the results and conclusions from the submitted …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

Here Come The Floods: Classification Of Rain-On-Snow Induced Flooding In Nevada, Emma Watts

Student Research Symposium

Given Nevada’s history of destructive flooding resulting from rain falling on mountainous snowpack, often called rain-on-snow (ROS) events, there is a great need to incorporate these events and their residual effects in infrastructure design methods. Examining relationships between USGS streamflow measurements and climate variables (specifically precipitation, temperature, and snowpack) obtained from neighboring SNOTEL stations provides means by which to classify ROS-induced floods from ROS events. Using both temperature and snowpack-based criterion to classify ROS events, this project differentiates between non-ROS and ROS-induced floods in a subset of USGS stations across the Sierra Nevada and reveals that ROS-induced floods produce, on …

Generating Optimal Space-Filling Designs With Particle Swarm Optimization, Rebekah Scott

Student Research Symposium

In 1935, Ronald Fisher published The Design of Experiments, establishing classical designs for various types of experiments. With the rise of computing power came optimal design, where statisticians can better customize designs according to the needs of the researchers running the experiment. This research focuses on generating optimal MaxMin space-filling designs with particle swarm optimization using various distance metrics (Manhattan, Euclidean, etc). Interestingly, changing the distance metric in the objective function had a minimal effect on the design, except for Aitchison geometry on the simplex. Space-filling designs are optimal for supporting high-order models with only a small sacrifice in prediction …

Introduction To Ensemble Watershed Segmentation, Scout Jarman

Student Research Symposium

Compared to color images, hyperspectral images are high dimensional, containing hundreds of channels of information. To distill this information, and capture spatial information, image segmentation is used to group similar pixels together. A popular image segmentation algorithm is the marker-based Watershed Transform. One difficulty with this algorithm is choosing the markers, or locations, that seed the algorithm. There are various approaches for automatic marker placement depending on the application, with little consensus on the most general method for hyperspectral images. We propose using an ensemble of random segmentations. Specifically, we investigate a simple, unbiased random marker placement strategy to generate …

Supplementary Files For "Adaptive Mapping Of Design Ground Snow Loads In The Conterminous United States", Jadon Wagstaff, Jesse Wheeler, Brennan Bean, Marc Maguire, Yan Sun

Browse all Datasets

Recent amendments to design ground snow load requirements in ASCE 7-22 have reduced the size of case study regions by 91% from what they were in ASCE 7-16, primarily in western states. This reduction is made possible through the development of highly accurate regional generalized additive regression models (RGAMs), stitched together with a novel smoothing scheme implemented in the R software package remap, to produce the continental- scale maps of reliability-targeted design ground snow loads available in ASCE 7-22. This approach allows for better characterizations of the changing relationship between temperature, elevation, and ground snow loads across the Conterminous United …

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 …

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.

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 …