Statistics and Probability Commons^™

Ground To Roof Snow Load Ratio (Gr) Data Release, Brennan Bean, Cooper Nelson, Jesse Wheeler, Scout Jarman, Salam Adil Al-Rubaye, Marc Maguire

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This data release provides historical ground-to-roof snow load ratio (GR) datasets used for snow load research and model development. The release includes original referenced datasets, cleaned country specific datasets, and a master dataset that combines Canadian and United States datasets into a standardized format for research and engineering applications.

Criticality In A Heterogeneous Neutron Transport Rod Model, Samuel Kaleb Crowford

All Graduate Reports and Creative Projects, Fall 2023 to Present

This work studies the stochastic behavior of neutron populations in a one-dimensional rod model using Monte Carlo simulation. The first part of this project reproduces the computational results of Dumonteil, Horton, Kyprianou, and Zoia (2025) by independently implementing the Monte Carlo algorithm described in their article, with the asymptotic behavior of the first moment analyzed in relation to the dominant eigenvalue and adjoint eigenfunction of the neutron transport operator. The model is then extended to a heterogeneous setting by introducing a central region where fission is suppressed. A global expectation over initial positions and directions is used to estimate the …

Mapler: An R Package For Estimating The Impact Of Climate Change On Maple Syrup Production, Matthew T. White

All Graduate Theses and Dissertations, Fall 2023 to Present

Successful maple sap tapping depends on the freeze/thaw cycle (i.e., temperatures fluctuating above/below freezing) during the winter and spring. Climate change threatens to alter the timing and duration of the tapping season. This necessitates research into how maple sap tapping will be impacted by climate change in order to help maple syrup producers prepare for the future. We define a sap day as a day where the freeze/thaw cycle occurred. Using information climate scientists use to predict future temperatures, we calculate how many sap days could occur each year. We develop software to analyze these sap day calculations to determine …

Learning Latent Structure In High-Dimensional Data Via Geometry And Graphs, Haozhe Chen

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern datasets often contain many measured variables for each observation, such as gene-expression levels, brain activity signals, or features in tabular data. These data are also often noisy, meaning that useful patterns are mixed with measurement error or irrelevant variation. Although such datasets can appear complex, they are frequently represented by simpler hidden structures, such as trajectories, clusters, or relationships between observations. This dissertation develops methods for uncovering these hidden structures by learning geometric and graph-based representations directly from data. The first part introduces Functional Information Geometry, which represents local patterns in high-dimensional data using functional features and constructs a …

Unifying And Expanding Global And Local Variable Importance Methods For Explainable Machine Learning, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning methods are powerful analytical tools used across all scientific disciplines and many other fields of investigation for prediction and inference from diverse data sources. Despite their broad applicability, machine learning methods are often highly complex and difficult to interpret. Developing a greater understanding of which variables most influence a response is essential for increasing the interpretability of these models and supporting informed decision-making. This research focuses on improving how we evaluate the importance of these variables.

One common approach is to shuffle the values of a variable and see how much the model accuracy gets worse. Another approach …

Spatial Prediction Under Uncertainty: Methodological And Computational Advances In Bayesian Maximum Entropy, Kinspride K. Duah

All Graduate Theses and Dissertations, Fall 2023 to Present

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that …

Constraint-Aware Metaheuristic Optimization For Experimental Design, Benjamin N. Fuller

All Graduate Theses and Dissertations, Fall 2023 to Present

Designing experiments becomes much more challenging when many variables and strict constraints are involved, as is common in modern science and engineering. This thesis introduces a new computational and mathematical framework that efficiently searches for optimal experiments in complex, high-dimensional spaces where traditional methods fail. By combining geometric techniques with flexible optimization algorithms like particle swarm optimization, our methods handle difficult constraints while scaling to real-world problems. Built in the high-performance Julia programming language and released as open-source software, this work bridges advanced theory with practical tools, offering researchers a powerful and accessible way to design better experiments under realistic …

Scalable Roof Polygon Extraction And Geometric Characterization From Remotely-Sensed Data For Snow Load Assessment, Jashon Newlun

All Graduate Theses and Dissertations, Fall 2023 to Present

Heavy snow accumulation on rooftops is a serious structural risk in cold climates, and understanding how much snow builds up on different types of roofs is essential for safe building design. Currently, most data on roof snow loads comes from small, labor-intensive field surveys that cover only a handful of buildings at a time. This results in far too few measurements of buildings to draw confident conclusions about how snow behaves across communities. This thesis develops and demonstrates a new automated approach for measuring roof snow accumulation and extracting key building characteristics across thousands of buildings at once using airborne …

Power Approximations With Non-Normal Data In Generalized Linear Mixed Models In R Using Steep Priors On Variance Components, Carlie Prinster, John Stevens

Mathematics and Statistics Student Research and Class Projects

ENAR Spring 2026 Conference presentation on Power Approximations with Non-Normal Data in Generalized Linear Mixed Models in R Using Steep Priors on Variance Components

Crime Statistics And Taxi Transportation In New York City: An Exploratory Data Analysis, Adelyn J. Fleming

All Graduate Reports and Creative Projects, Fall 2023 to Present

In a heavily populated city as busy and vibrant as New York City, people are constantly on the move. Some of that movement might be connected to the occurrence of certain crimes. This study explores how movement, especially from yellow taxicabs, relates to crime occurrences within different parts of the city. By looking at the 2018 taxi trip and crime data, alongside population data from the 2020 U.S. Census, this project aims to explore how individuals travel within the city and whether there is any relationship with the types of crime that occur within those areas. Visual tools and maps …

Error Reduction Methodology And Data Simulation For Interval Data, Ranik Christopher Jelinek

Undergraduate Honors Capstone Projects

Chronic kidney disease (CKD) is a progressive condition affecting hundreds of millions of individuals worldwide. However, clinical datasets often record continuous laboratory measurements as categorical intervals rather than precise numerical values. This interval-censored structure presents methodological challenges for standard regression-based classifiers. This study compares three strategies for handling interval-valued predictors prior to fitting a logistic LASSO model: (1) midpoint imputation, which replaces each interval with its arithmetic center; (2) ordinal encoding, which maps intervals to integer ranks; and (3) a Monte Carlo simulation approach, which repeatedly samples uniformly from each observed interval and averages predictions across replications. Using a 10-fold …

The Impact Of Transmission Thresholds Across Multiple Scales On The Spread Of Chronic Wasting Disease In Wisconsin, Jen Mcclure

All Graduate Theses and Dissertations, Fall 2023 to Present

Wildlife diseases can be difficult to control once they are established. This is especially true when they spread through contact with infectious material left in the environment. One such disease is chronic wasting disease (CWD), a fatal illness affecting deer and related species in North America and other regions. CWD is caused by prions, misfolded proteins that can remain infectious for years after shedding by infected hosts.

Recent research shows that CWD infection does not always follow from the gradual accumulation of prions through small contact events. Rather, an individual may need to encounter a certain prion dose all at …

Implications Of The Attenuated Allee Effect On Population Dynamics, Dana Strong

All Graduate Theses and Dissertations, Fall 2023 to Present

The Allee effect is an ecological phenomenon characterized by a per capita growth rate that increases as the population size increases in the context of low population density. The Allee effect can lead to rapid extinction events. Consequently, ecologists can attempt to control the strength of the Allee effect to help increase the population (in the case of endangered species) or decrease the population (in the case of parasites or pests).

This research aimed to study not the strength of the Allee effect, but the intensity of the Allee effect, or how rapidly cooperation between individuals causes the per capita …

Machine Learning Applications: Cell Tracking And Nonparametric Estimation Of Non-Smooth Divergences, Mina Mahbub Hossain

All Graduate Theses and Dissertations, Fall 2023 to Present

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or …

Tannin Supplementation Alters Foraging Behavior And Spatial Distribution In Beef Cattle, Bashiri Iddy Muzzo, R. Douglas Ramsey, Kelvyn Bladen, Juan J. Villalba

Wildland Resources Student Research

Beef production on chemically uniform grass monocultures can limit nutrient synchrony and contribute to uneven pasture use. We evaluated whether supplementing tannins with bioactive plant secondary compounds improves foraging dynamics and landscape use by beef cattle grazing a meadow bromegrass monoculture in ways aligned with rangeland sustainability. Twenty-four Angus cow–calf pairs were allocated to six 3.6-ha paddocks (four pairs/paddock), randomly assigned to Control (Ctrl; n = 3) or Tannin treatment (TT; n = 3). Animals received 1 kg/cow/day of DDGs, with TT receiving an added 0.4% tannins (2:1 condensed:hydrolyzable). Grazing occurred during four 15-day periods (July– September) across two years. …

Quantifying The Sensitivity Of Land Use Land Cover Metrics Through Simulation Techniques, Haley Burger

All Graduate Theses and Dissertations, Fall 2023 to Present

As human activities and climate change continue to reshape our landscape, understanding how land use changes over time is becoming increasingly important. Accurate ways to track and analyze these changes are essential for governments, businesses, and communities to make informed decisions. Monitoring agricultural land is particularly critical, as shifts in land use can impact food production and environmental pollutants. One of the primary tools used in the United States to monitor agricultural land is the Cropland Data Layer (CDL), an annual map created by the United States Department of Agriculture (USDA) from satellite images. While the CDL is highly accurate, …

Unveiling Insights From Complexity: Advanced Computational Techniques For High-Dimensional Medical Data, Devin P. Eddington

All Graduate Theses and Dissertations, Fall 2023 to Present

Healthcare generates vast amounts of data daily, from genetic profiles to hospital records, but much of it remains untapped due to its complexity. This dissertation develops new computational tools to unlock this data’s potential, aiming to improve patient care and medical research. Five projects tackle different challenges: Project 1 creates Deep MAGIC, a method to fill in missing genetic and image data accurately, vital for understanding diseases like cancer. Project 2 analyzes how the COVID-19 pandemic disrupted surgeries, finding a 27% drop and temporary complication rises in 2020, guiding future crisis planning. Projects 3 and 4 study kidney disease trials, …

Graph-Based Machine Learning: Higher-Order Interactions, Guided Generation, And Knowledge-Graph Tools, Thomas J. Kerby

All Graduate Theses and Dissertations, Fall 2023 to Present

This dissertation brings the power of graph thinking to three key challenges in modern AI, making complex data more transparent, generative design more controllable, and scholarly exploration more intuitive. First, we introduce Local CorEx, a new machine learning technique that uncovers hidden relationships among variables, making it easier to understand complex datasets without heavy computation. Next, we show how to guide the creation of new molecules by viewing the generation process itself as a walk through a "state graph," letting researchers steer outcomes toward desired chemical properties—without any extra model training. Finally, we deliver an open-source toolkit that builds interactive …

Empirical Evaluation Of Bayes Error Rate Bounds In Binary Classification, Riley May

All Graduate Theses and Dissertations, Fall 2023 to Present

Classification tasks are fundamental in statistical machine learning. In classification tasks, a general goal is to build or select a model that can correctly classify data with as few errors as possible. However, for a particular dataset, the minimal number of errors achievable is seldom zero since overlap in the data makes errors unavoidable. As a result, it is often difficult for machine learning practitioners and data scientists to know whether classification errors can be reduced through further refinement. A potential solution to this lies in the Bayes error rate (BER). The BER is the lowest error rate achievable for …

Aleci: An R Package For Non-Parametric Confidence Intervals On Accumulated Local Effects Plots, Matthew R. Lister

All Graduate Reports and Creative Projects, Fall 2023 to Present

Machine learning models can take a collection of inputs and craft an output. The mathematical formulas these models use to calculate their outputs easily become too complex or time consuming for a human to analyze. Collectively, we refer to these as black box models. Accumulated local effects plots (ALE) are a method for adding interpretability and visibility into the effects that individual variables contribute to the predictions made by black box models. The method designed by D.W. Apley calculates equally spaced point estimates of the response value to construct a graph across the range of the variable of interest. AleCI …

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

Designing Accessible And Dependable Tools For Vocational Rehabilitation Data Analysis, Ruth E. Taylor

All Graduate Theses and Dissertations, Fall 2023 to Present

Since 1973, the U.S. Rehabilitation Services Administration (RSA) has partnered with state vocational rehabilitation (VR) agencies to help individuals with disabilities achieve meaningful employment and independence. RSA-911 datasets play a crucial role in this effort by capturing detailed participant data, but their complexity can hinder effective analysis.

To simplify this process, we present an R software package to streamline the cleaning and analysis of RSA-911 and Transition Readiness Toolkit (TRT) data, a new measure of program effectiveness. We also deliver a user-friendly dashboard, empowering both VR researchers and counselors with the opportunity to conduct analyses. Using our developed tools, we …

Gig Drivers Need Access To Affordable Electric Vehicles (Evs) And Accessible, Fast Chargers, William Bouck

Research on Capitol Hill

Compared to gas cars, EVs are cheaper to fuel and maintain, and they don’t pollute Utah’s air. But they aren’t used on a scale big enough to make a difference. We asked gig drivers (people who work for Uber, Grubhub, etc.) why EVs aren’t catching on, since they spend 30+ hour driving per week. Addressing their problems will enable increased EV use, making travel cheaper and cleaner.

Supplementary Files For: "Structure Identification For High-Dimensional Data In The Vicinity Of Bear Lake", Ben Shaw, Haley Burger, Brennan Bean, Kevin Moon

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This report focuses on seven water quality measurements taken at 43 different depths on the Bear Lake for the months of June - November in the years 2018 - 2023. These measurements create a high-dimensional dataset on which we apply state-of-the-art machine learning (ML) techniques to look for low-dimensional structure in the data. A similar effort was made for weather measurements taken near the lake. Our analysis revealed that water quality measurements tend to cluster (i.e., group together) by year, while weather measurements tend to cluster by time of the year. This suggests that the structure observed in the water …

Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Emma M. Watts

All Graduate Theses and Dissertations, Fall 2023 to Present

Serious flooding can happen when rain falls on snow, which we call a rain-on-snow (ROS) event. Increasing our understanding of the behavior of floods resulting from ROS events can help us design better systems to manage flood water and prevent it from causing damage. This thesis explores how ROS events affect streamflow in the Western United States by examining the weather conditions that precede a streamflow surge. We classify stream surges as ROS or non-ROS induced based on these weather conditions, which helps us separate floods caused by ROS events from those caused by other factors. By comparing these different …

Impact Of Snow Accumulation On Structural Integrity: Present And Future Perspectives, Kenneth K. Pomeyie

All Graduate Theses and Dissertations, Fall 2023 to Present

In the United States, accommodating the weight of accumulated snow on buildings is a crucial consideration in building design. Engineers are tasked with determining the design snow load, which is defined as the weight of accumulated snow that a structure should withstand to limit the risk of building collapse to an acceptably low level. Typically, this process involves analyzing historical data of the annual maximum snow accumulations for each snow season. However, accurately assessing these design snow loads entails navigating through a series of statistical challenges. This dissertation, composed of three papers, is dedicated to addressing these statistical hurdles in …

Supplementary Files For: Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Emma Watts, Brennan Bean

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Serious flooding can happen when rain falls on snow, which we call a rain-on-snow (ROS) event. Increasing our understanding of the behavior of floods resulting from ROS events can help us design better systems to manage flood water and prevent it from causing damage. This thesis explores how ROS events affect streamflow in the Western United States by examining the weather conditions that precede a streamflow surge. We classify stream surges as ROS or non-ROS induced based on these weather conditions, which helps us separate floods caused by ROS events from those caused by other factors. By comparing these different …

Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations, Gideon Parry

All Graduate Theses and Dissertations, Fall 2023 to Present

Reliability target loads refer to the amount of accumulated snow a roof needs to be able to support to ensure that the probability of collapse is sufficiently low. Since ground snow weight, or load, is much easier to measure than roof snow load, models for roof snow loads rely on ground snow load measurements along with a statistical model that estimates roof snow retention as a ratio of the measured ground snow load. This thesis focuses on improving the roof snow retention model using data from Canadian case studies that include information about building geometry and local wind speeds. This …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

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Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Supplementary Files For: "Interactive Modeling Of Bear Lake Elevations In A Future Climate", Benjamin D. Shaw, Scout Jarman, Brennan Bean, Kevin R. Moon, Wei Zhang, Nathan Butler, Tommy Bolton, April Knight, Emeline Haroldsen, Abby Funk, Rebecca Higbee

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The water level, or elevation, of Bear Lake has a significant impact on agriculture, power, infrastructure, and recreation for communities around the lake. Climatological variables, such as precipitation, temperature, and snowfall, all have an impact on the elevation of Bear Lake. As the climate changes due to greenhouse gas emissions, the typical behaviors of these climate variables change, leading to new behaviors in Bear Lake elevation. Because of the importance of Bear Lake, it is vital to be able to model and understand how Bear Lake's elevation may change in the face of different climate scenarios and to gain further …