Statistics and Probability Commons^™

An Association Test For Ordinal Outcomes In Clustered Data With Informative Cluster Size, Hasika K. Wickrama Senevirathne, Sandipan Dutta

Mathematics & Statistics Faculty Publications

In cluster-correlated data, the number of observations in a cluster can be associated with the outcome from that cluster. This phenomenon is known as informative cluster size which can occur in cluster-randomized clinical trial data. Several studies have found that ignoring the issue of informative cluster size can produce biased results in the analysis of clustered data. Most of the existing methods for addressing informative cluster size are suited to continuous outcomes. However, ordinal outcomes and covariates are often encountered in clustered data obtained from large clinical studies. The existing methods for ordinal association testing in clustered data can produce …

Factorial Design: A New Look Through Overlap Measures, Sarah W. Liebenow

College of Graduate Studies: Theses & Dissertations

Traditional factorial analysis often relies on ANOVA, which assumes normality and equal variances. This thesis presents a nonparametric approach for assessing main and interaction effects in a 2 × 2 factorial design using the overlap coefficient, estimated through kernel density methods. A bootstrap procedure is used to approximate its sampling distribution for hypothesis testing. Simulation studies compare the overlap-based test with the ANOVA F-test, permutation F-test, and the Kruskal–Wallis test under heteroskedasticity and non-normal conditions. Results show that the overlap measure is highly sensitive to differences in spread and shape, detecting effects that traditional methods frequently miss.

Serum Biomarker Trajectory Clusters Predict Functional Outcome And Quality Of Life For Traumatic Brain Injury, Thanh Son Do, Chantal Carnes, Zhihui Yang, Firas Kobeissy, Hamad Yadikar, Gayla R. Olbricht, Olli Tenovuo, Jussi P. Posti, Ewout W. Steyerberg, Lindsay Wilson, Nicole Von Steinbüchel, Endre Czeiter, Andras Buki, David K. Menon

Mathematics and Statistics Faculty Research & Creative Works

Serum brain-enriched biomarkers are increasingly employed in the clinical evaluation of traumatic brain injury (TBI) to assist with triage, neuroimaging decisions, and prognostication. However, the potential of temporal biomarker trajectories to inform disease monitoring and long-term outcomes remains underexplored. We aim to identify distinct biomarker trajectory (TRAJ) profiles in traumatic brain injury patients and to examine their associations with long-term clinical outcomes. The study included 373, CT-positive Intensive Care Unit (ICU) traumatic brain injury patients (256 with initial Glasgow Coma Scale 3–12) from the Collaborative European Neurotrauma Effectiveness Research in TBI (CENTER-TBI) core study who had at least two serum …

Establishing A Public Health Surveillance System For The Opioid Crisis: The Experience Of The Healing Communities Study, Bridget Freisthler, Daniel J. Feaster, Charles Knott, Marc Larochelle, John Mccarthy, Svetla Slavova, Sharon L. Walsh, Jennifer Villani

Biostatistics Faculty Publications

Introduction: Efforts to reduce opioid overdose deaths in the United States have been stymied by the lack of timely and standardized population-level data for local, state, and national levels. The U.S. has a strong national need for linking opioid and other drug overdose surveillance data to service utilization data for overdose prevention and treatment to inform resource allocation and response planning.

Methods: We provide insight on the challenges of identifying, obtaining, and harmonizing administrative outcome data across four states using the collective experience from the HEALing Communities Study to test a community-engaged, data-driven, population-level intervention to reduce opioid overdose deaths. …

Type Ii Diabetes Treatment Comparison Via Compartment Modeling, Abigail M. Collins

Theses and Dissertations

Type II diabetes mellitus affects one in ten adults worldwide, yet the effects of treatment type and adherence level on developing complications and quality of life have not been well characterized at the population level, and mathematical modeling offers a structured way to examine these dynamics. This thesis adapts the Boutayeb et al. (2004) model to incorporate dynamic treatment types and levels of adherence, producing nine scenarios in which complication development rate and complication recovery rate differed, to compare peak complications and quality of life across treatment and adherence conditions. Using a system of ordinary differential equations and compartment modeling, …

Uncertainty Quantification, Propagation & Conjunction Assessment In Orbital Mechanics Using Generalized Polynomial Chaos Expansion & 2-Dimensional Conjunction Plane Analysis Techniques, Monalisa Karim

Mechanical and Aerospace Engineering Theses

Uncertainties, that are inherent to dynamic models, can be associated with state initial conditions, force modelling errors, navigation and actuation errors. In system modelling stochastic differential equations are used to represent dynamic phenomena with uncertainties, for which the solutions are probability density functions of quantities of interest characterizing the realization of the stochastic processes. In Polynomial Chaos Expansion (PCE) propagation, these solutions are represented as weighted sums of multivariate spectral polynomials that are functions of the input random variables. Generalized polynomial chaos expansion (gPC) is an extension to the original homogenous PCE which projects the random solution onto a basis …

Supplemental Bibliographic Details. From 2001 Mars Odyssey To Earth’S Climate Crisis: Integrating Gamma Spectroscopy, Martian Soil Simulants, And Plant Genomes For Agroecology, Anchored In Sri Lanka’S Mars-Context Serpentinites, Suniti Karunatillake, Maheshi Dassanayake, Carlos Gary Bicas

Planetary Science Lab

Bibliographic details follow to supplement hyperlinked citations in the multinational GANGOTRI-supporting project conceived by Karunatillake, Dassanayake, and Gary-Bicas

Guidelines For Standard Basic Notations In Applied Statistics, Abhaya Indrayan, Shivani Saini Ms

COBRA Preprint Series

Whereas some statistical notations are standard and uniformly used by different workers, many are not. Varying notations lead to confusion among the readers, particularly those engaged with applied statistics material, such as medical professionals. This communication proposes that all basic notations be standardized so that the same notations are consistently used by different authors, in different books, journals, and articles for the benefit of those who are not rigorously trained statisticians. Guidelines for such standard notations are also provided. The lead must be taken by statisticians.

Predicting Criminal Behavior In Major Us Cities, Madison A. Price

SPARK Symposium Presentations

In recent years, especially post pandemic, there has been a decrease in crime in the United States. Unfortunately, the country’s violent crime rates are still significantly higher compared to similar high-income countries, so what predicts crime in major American cities? There is tons of research to support the idea that demographics can offer some insight into predicting crime. There are countless online resources that seek to identify major crime centrals in the United States (Petrino, 2025). In the late 1990s, researchers noticed that crime rates in cities had a downward slope due to an important contributor: demographic change (Fox & …

Investigating The Role Of Humic Acid In The Adsorption Mechanics Of Acetaminophen On Potassium Persulfate-Aged Polyethylene Terephthalate (Pet), Andrew Littleton, Maria Danielle Garrett, Phd

SPARK Symposium Presentations

Pharmaceutical contaminants such as acetaminophen (APAP) are showing a rising presence in aquatic environments, where their interactions with microplastics (MPs) can potentially modulate natural degradation mechanisms. Concurrent presence of the two substances has been shown to potentiate increase their individual harmful effects. This study investigates whether oxidative aging and humic-acid surface modification of PET microplastics influence APAP adsorption.

In this study, UV-aging was reproduced using an iron (II)-activated potassium persulfate (Fe(II)-KPS) oxidation system. Aqueous dissolved organic matter (DOM) is simulated using multi-hour exposure to humic acid. The MPs are then removed from the solution to examine adsorption mechanisms. While most …

Investigating The Connection Between Als Through The Mutation R522s In The Rna Binding Protein, Dennia Estrella-Vargas, Lydia Uptain

Mathematics

Amyotrophic lateral sclerosis (ALS) is a fatal disease that causes the deterioration of motor neurons , death is usually due to respiratory paralysis. The variant R522S was chosen because it is near a hot spot of pathogenic variants. It is an arginine-to-serine swap, this swap is present in pathogenic variants near the 522 position, such as R514S, R521S, R524S. Recent evidence suggests that arginine-deficiency can influence disease progression.

Data-Driven Partitioning In Distributed Optimization For Networked Systems, Prosper Azameti

Theses and Dissertations

The convergence behavior of distributed optimal power flow (OPF) depends strongly on how the power network is partitioned into regions. Classical graph-based methods such as METIS are widely used, but they rely mainly on static topological criteria and do not explicitly incorporate operating-point-dependent information that may affect distributed optimization performance. This thesis develops a data-driven partitioning framework for distributed OPF using graph neural networks (GNNs). Each OPF scenario is represented as a graph in which buses are nodes and transmission lines are edges. Node and edge features capture both structural and operational characteristics of the network. Partition prediction is formulated …

Using Camera-Based Unmarked Spatial Capture-Recapture Modeling To Estimate Reintroduced Elk (Cervus Canadensis) Population Parameters And Distribution In Southeastern Kentucky, Claire Marie Muia

Theses and Dissertations--Forestry and Natural Resources

Estimation of population parameters is important for wildlife management decisions. Elk reintroduced to southeastern Kentucky experienced early irruptive population growth and are currently monitored using a statewide harvest-based statistical population reconstruction model (SPR) across the Kentucky Elk Restoration Zone (KERZ). Because the SPR model is spatially coarse and difficult to scale to the smaller management units comprising the KERZ, we conducted a spatially explicit capture-recapture study using a clustered camera-trapping array deployed for 10 weeks from June–August 2024 to estimate elk population parameters within Management Unit 4. Due to a lack of resights of GPS-marked elk, population parameters were estimated …

Teaching Effectiveness On Secondary Mathematics: Evidence From Pisa—Shanghai-China, Ting Shen

Psychological Science Faculty Research & Creative Works

Educational researchers and policymakers around the world have a strong interest in understanding the underlying reasons for the remarkable academic achievement of Chinese students in the Programme for International Student Assessment (PISA). Although teachers have a significant impact on student achievement, empirical evidence on teaching effectiveness in the Chinese education system has been scarce. This study uses the PISA 2012 Shanghai-China data and employs both multilevel models and quantile regression models to investigate effective teaching factors and their differential effects for students at different mathematics achievement levels. The results reveal the importance of cognitive activation and disciplinary climate as consistent, …

Assessing The Diversity And Composition Of Crayfish Assemblages In The Ogeechee River Basin, Reginald Turner

College of Graduate Studies: Theses & Dissertations

Crayfish assemblage composition in the southeastern United States is understudied relative to other aquatic taxa, such as aquatic insects and fishes, and the Coastal Plain watersheds of that region are particularly underrepresented in the contemporary literature on this topic. For example, although 38% of the crayfish species in Georgia are considered “species of greatest conservation need,” most of the distributional data used to make these designations are outdated, with some dating back over 50 years. This thesis sought to update our understanding of the contemporary distributions of crayfish species within the Ogeechee River Basin (ORB), a watershed in southeastern Georgia …

Equilibrium Stability Under Nuclear Confrontation, Martin Bohner, A. A. Martynyuk

Mathematics and Statistics Faculty Research & Creative Works

This article proposes and analyzes mathematical models of confrontation between two and n countries, including countries with nuclear weapons. The proposed models are based on a generalization of Richardson's well-known mathematical model of the arms race. Namely, the factor of hostility is filled with expanded content, including public opinion and the armed forces of the opposing countries. Qualitative analysis of confrontation models is carried out by the method of Lyapunov functions and by applying nonlinear integral inequalities. As a result of the analysis, the conditions for the stability of the equilibrium state of the opposing countries are established, and the …

Threshold Asymmetric Conditional Autoregressive Range (Tacarr) Model, Isuru Ratnayake, V. A. Samaranayake

Mathematics and Statistics Faculty Research & Creative Works

This paper introduces a Threshold Asymmetric Conditional Autoregressive Range (TACARR) model for analyzing the daily price ranges of financial assets. The proposed formulation assumes that the conditional expected range switches between two regimes, representing upward and downward market states, with the disturbance distribution also allowed to vary across regimes. A self-adjusting threshold component, determined by past values of the series, is used to identify the prevailing market regime. In this way, the model is able to capture asymmetric and heteroscedastic volatility behavior in financial markets. The TACARR model is designed to address several limitations of existing price range models, including …

A Variance Decomposition Approach To Inconclusives In Forensic Black Box Studies, Amanda Luby, Joseph B. Kadane

Mathematics and Statistics Faculty Work

In the USA, ‘black box’ studies are increasingly being used to estimate the error rate of forensic disciplines. A sample of forensic examiner participants is asked to evaluate a set of items whose source is known to the researchers but not to the participants. Participants are asked to make a source determination (typically an identification, exclusion, or some kind of inconclusive). We study inconclusives in two black box studies, one on fingerprints and one on bullets. Rather than treating all inconclusive responses as functionally correct (as is the practice in reported error rates in the two studies we address), irrelevant …

Barriers To Immunity: Understanding Covid-19 Vaccine Uptake In Africa, Emilia Blechschmidt

Honors Theses

This thesis examines the factors influencing COVID-19 vaccine uptake across African countries, with a focus on structural, informational, and behavioral barriers to immunization. Drawing on cross-country data, the study analyzes how access to transportation, reliable information, and healthcare resources shape vaccination rates, alongside the effect of demographics and institutional factors in shaping individual perceptions of risk and vaccine safety.

The findings emphasize that the broader strength and preparedness of national health systems strongly influence vaccine uptake. Countries that demonstrated higher coverage of routine childhood immunizations, such as polio and hepatitis B, also tended to perform better in COVID-19 uptake efficiency …

Feasibility, Acceptability, And Preliminary Efficacy Of A Pilot Study To Integrate Buprenorphine Into A Harm-Reduction Drop-In-Center In Kampala, Uganda, Julia Dickson-Gomez, Sergey Tarima, Wamala Twaibu, Dan Katende, Latifah Kyeswa, Laura Glasman, Arthur Kiconco, Sarah Krechel, Bryan Johnston, Moses Ogwal, Brian Byamah Mutamba, Peter Mudiope, Stella Alamo, Rhoda Wanyenze, Geofrey Musinguzi

Biostatistics Faculty Publications

Illicit drug use has been increasing rapidly in Sub-Saharan Africa in the past decade. However, until recently HIV prevention has largely ignored people who inject drugs and medications to treat opioid use disorder (MOUD) were largely absent. This paper reports results of a pilot intervention that integrated buprenorphine into a harm-reduction drop-in-center for people with opioid use disorder (OUD) in Kampala, Uganda. We collected implementation outcomes and changes in self-reported drug use after buprenorphine initiation. We conducted qualitative interviews with a subset of 14 participants who had initiated buprenorphine. Sixty-two participants were screened for OUD, of whom 57 were eligible …

Artificial Intelligence In Biomedical Team Science: Perceptions, Practices, And Training Needs, Emily Slade, Kelsey N. Karnik, Caitline Phan, Megan E. Hall, Yana Feygin, Kristen J. Mcquerry

Biostatistics Faculty Publications

Introduction: Artificial intelligence (AI) is increasingly used in biomedical research, yet limited empirical work has described how researchers use AI tools on collaborative research teams and how they view their role within team-based research. This study examines researchers’ experience with and attitudes toward AI use in collaborative research environments.

Methods: A cross-sectional survey was administered to 178 investigators engaged in collaborative research at the University of Kentucky. Questions assessed AI use across research and communication tasks, team-related decision-making practices, perceived benefits and concerns, and preferences for training and frameworks.

Results: Thirty-nine participants responded (22%). AI use was heterogeneous: 26% had …

Designing A Research Study: Controlling For A Variable And Using Chatgpt, Fritz Umbach

Open Educational Resources

This assignment uses a hypothetical society to help students understand the idea of “controlling for a variable” and practice applying it to a real-world research question. Students design a research approach to examine whether income differences are better explained by family background or by systemic prejudice, working within clear data limits. ChatGPT is used as a research guide to help students brainstorm, test, and revise their methods, while encouraging them to critically evaluate the usefulness and limits of AI-generated suggestions. The assignment emphasizes careful reasoning, clear research design, and thoughtful use of AI as a support for learning rather than …

Enhancing Team Science By Training Collaborative Biostatisticians To Have A Strong Statistical Voice, Gina-Maria Pomann, Steven C. Grambow, Marissa C. Ashner, Bibhas Chakraborty, Nan Liu, Megan L. Neely, Sarah Peskoe, Lacey Rende, Emily Slade, Tracy Truong, Lexie Zidanyue Yang, Greg P. Samsa, Jesse D. Troy

Biostatistics Faculty Publications

Strong statistical voice is defined as the ability to advocate and negotiate for good and ethical statistical practices, including integrating and resolving differing scientific approaches. This skill is crucial for biostatisticians who work on biomedical research teams, as it ensures the integrity and accuracy of statistical analyses and fosters productive collaborations with non-statisticians. Despite its importance, new graduates often lack targeted training opportunities. This manuscript presents a scalable training approach through the development of online videos. Preliminary didactic materials focused on two key applications: providing written comments on manuscripts and engaging in study design discussions. To evaluate this training approach, …

Modeling Rank Distribution And The Relative Importance Factor Index In Discrete Power-Law Models: Application To Social Resilience Using The Scopus Database, Brian Llinas, Jose Padilla, Humberto Llinas, Erika Frydenlund, Katherine Palacio

VMASC Publications

Prior research on power-law distributions has primarily focused on modeling frequency patterns, with less attention given to rank distributions and how ranked positions reflect relative importance among elements. In discrete power-law distributions, frequency-based metrics often provide limited discrimination in the tail, where elements may exhibit similar counts but differ in relative dominance. These patterns are especially evident, for instance, in academic publishing, where keywords, affiliations, and citations commonly exhibit power-law behavior. To address this limitation, we introduce the Relative Importance Factor (RIF) Index, a statistical measure derived from the estimated discrete power-law rank distribution rather than an additional independent parameter. …

Multiple Changepoint Detection For Non-Gaussian Time Series, Robert Lund, Thomas J. Fisher, Norou Diawara, Michael Wehner

Mathematics & Statistics Faculty Publications

This article combines methods from existing techniques to identify multiple changepoints in non‐Gaussian autocorrelated time series. A transformation is used to convert a Gaussian series into a non‐Gaussian series, enabling penalized likelihood methods to handle non‐Gaussian scenarios. When the marginal distribution of the data is continuous, the methods essentially reduce to the change of variables formula for probability densities. When the marginal distribution is count‐oriented, Hermite expansions and particle filtering techniques are used to quantify the scenario. Simulations demonstrating the efficacy of the methods are given and two data sets are analyzed: 1) the proportion of home runs hit by …

An Ensemble Classifier For Ordinal Outcomes In High-Dimensional Genomics Data, Heranga K. Rathnasekara, Sinjini Sikdar

Mathematics & Statistics Faculty Publications

Analysis of genomics data for predicting disease outcomes is a fast-growing field in medical research. There often exist categorical, specifically, ordinal outcomes that need to be predicted based on genomic profiles. This has led to recent development of some high-dimensional ordinal classification methods that can address the large dimensionality of the genomic covariate set. These high-dimensional ordinal models tend to vary widely in their performance depending on the data they are applied to and the evaluation criteria used. In this article, we outline an ensemble ordinal classifier that integrates different ordinal modeling approaches through bootstrap-based model evaluation, multi-metric performance assessment, …

Beyond The Lace Index: Benchmarking Machine Learning Architectures And Explaining 30-Day Hospital Readmission Risk With Shap Analysis, Carl E. Hughes Iii

Williams Honors College, Honors Research Projects

Unplanned 30-day hospital readmission remains a fundamental challenge in US healthcare, associated with increased risk to patient recovery and representing an estimated $52.4 billion in annual expenses (Beauvais et al., 2022). While the rigorously validated LACE index serves as the clinical standard for readmission modeling, its linear structure and four explanatory variables lack the complexity to capture the high-dimensional and interactive nature of patient risk. This study utilizes an admission granularity level cohort of the MIMIC-IV database to develop and compare machine learning architectures against the baseline LACE index. Due to the imbalanced prevalence of readmission, the penalized logistic regression, …

Modeling Housing Prices: Which Features Matter Most?, Alex Ruvolo

Williams Honors College, Honors Research Projects

This paper attempts to find the biggest factors and traits that influence the cost of housing. This will include the lot size, type of street, utilities, neighborhood, year built, heating, electrical, yard size, number of different rooms, age, condition, and others. I will attempt to answer the question of whether the prices of houses have changed within the last 5 to 10 years, and obviously this is an easy question to answer. However, the bigger question beyond this is are the main factors affecting housing prices all important in explaining this relationship? Is one factor more important than the rest …

Flavor, Transverse Momentum, And Azimuthal Dependence Of Charged Pion Multiplicities In Semi-Inclusive Deep-Inelastic Scattering With 10.6 Gev Electrons, P. Bosted, H. Bhatt, S. Jia, W. Armstrong, D. Dutta, R. Ent, D. Gaskell, E. Kinney, H. Mkrtchyan, S. Ali, R. Ambrose, D. Androic, C. Ayerbe Gayoso, A. Bandari, V. Berdnikov, D. Bhetuwal, D. Biswas, M. Boer, E. Brash, A. Camsonne, M. Cardonna, J. P. Chen, J. Chen, M. Chen, E. M. Christy, S. Covrig, S. Danagoulian, M. Diefenthaler, B. Duran, C. Elliot, H. Fenker, E. Fuchey, J. O. Hansen, F. Hauenstein, T. Horn, G. M. Huber, M. K. Jones, M. L. Kabir, A. Karki, B. Karki, S. J. D. Kay, C. Keppel, V. Kumar, N. Lashley-Colthirst, W. B. Li, D. Mack, S. Malace, P. Markowitz, M. Mccaughan, E. Mcclellan, D. Meekins, R. Michaels, A. Mkrtchyan, C. Morean, G. Niculescu, I. Niculescu, B. Pandey, S. Park, E. Pooser, B. Sawatzky, G. R. Smith, H. Szumila-Vance, A. S. Tadepalli, V. Tadevosyan, R. Trotta, H. Voskanyan, S. A. Wood, Z. Ye, C. Yero, X. Zheng, Hall C Sidis Collaboration

Physics Faculty Publications

Measurements of semi-inclusive deep-inelastic scattering multiplicities for 𝜋⁺ and 𝜋⁻ from proton and deuteron targets are reported on a grid of hadron kinematic variables 𝑧, 𝑃𝑇, and 𝜙* for leptonic kinematic variables in the range 0.3< 𝑥< 0.6 and 3< 𝑄²< 5GeV². Data were acquired in 2018 and 2019 at Jefferson Lab Hall C with a 10.6 GeV electron beam impinging on 10-cm-long liquid hydrogen and deuterium targets. Scattered electrons and charged pions were detected in the High Momentum Spectrometer and Super High Momentum Spectrometer, respectively. The multiplicities were fitted for each bin in (𝑥,𝑄²,𝑧,𝑃_𝑡) to extract the 𝜙*—independent 𝑀₀ and the azimuthal modulations ⟨cos⁡(𝜙*)⟩ and ⟨cos⁡(2⁢𝜙*)⟩. The 𝑃_𝑡 dependence of the 𝑀₀ results was found to be remarkably consistent for the four cases studied: 𝑒⁢𝑝→𝑒⁢𝜋⁺⁢𝑋, 𝑒⁢𝑝→𝑒⁢𝜋^−⁢𝑋, 𝑒⁢𝑑→𝑒⁢𝜋⁺⁢𝑋, 𝑒⁢𝑑→𝑒⁢𝜋^−⁢𝑋 over the range 0GeV< 𝑃_𝑡< 0.4GeV, as were the multiplicities evaluated near 𝜙*=180∘ over the extended range 0GeV< 𝑃_𝑡< 0.7GeV. The Gaussian widths of the 𝑃𝑡 dependence exhibit a quadratic increase with 𝑧. The cos⁡(𝜙*) modulations were found to be consistent with zero for 𝜋⁺, in agreement with previous world data, while the 𝜋⁻ moments were, in many cases, significantly greater than zero. The cos⁡(2⁢𝜙*) modulations …

Infimum Dimension Nash Embeddings For 2d Projective Shape Analysis, Robert L. Paige, Vic Patrangenaru

Mathematics and Statistics Faculty Research & Creative Works

Vector embeddings make complicated data extracted from networks, words and images, more amendable to data science applications. At the present time, the Veronese-Whitney (VW) matrix embedding of the real projective space is the state of the art for making inference about digital images from an uncalibrated camera, such as a cell phone or security camera. In this work we consider vector embeddings for the projective shape data and in particular determine the minimum dimension isometric (distance-preserving or Nash) vector embedding for a projective space. We determine such an embedding for the projective plane in closed-form. From this embedding we determine …