Statistics and Probability Commons^™

Using Effect Sizes, Confidence Intervals, And The Bayes Factor To Better Understand The T-Test, Analysis Of Variance, And Regression Results, Holmes Finch

Perspectives on Early Childhood Psychology and Education

Null hypothesis testing is a widely used paradigm for assessing research hypotheses across the social sciences. Despite their ubiquity, researchers have discussed a number of problems and limitations to hypothesis testing and have suggested alternatives that might provide greater depth and explanation of research results. The purpose of this paper is to describe the use of several such alternatives and to show how they can be integrated with one another and with null hypothesis testing in order to provide a more holistic view of research hypotheses.

A Statistical Analysis Of Current And Future Hurricane Activity In The North Indian Ocean, Basil Lund

2026 Symposium

A hurricane is defined as a tropical storm with winds sustained at 74 mph or greater. I examined major (category 3 and above) hurricane activity over the North Indian Ocean from the years 1972-2019 as reported by Colorado State University Hurricane Forecast Archive. Using RStudio, I conducted a binomial analysis of the CSU dataset to calculate probabilities of zero to ten years with one or more major North Indian Ocean hurricanes in the next decade. I conducted a geometric analysis to determine probabilities associated with waiting periods for the next year with a major hurricane, as well as a Poisson …

Developing A Comprehensive Resource Guide For Caregivers Within The Area Agency On Aging, Aiden R. Murphy

Public Health Capstone Projects

This project developed a new universal caregiver resource guide for caregivers within the Area Agency on Aging, in order to improve resource navigation and workflow efficiency. Resources were collected, verified, and organized into a new, streamlined guide via the ARIA chatbot, covering multiple needs. Caregiver resources were collected and verified by the capstone student and mentor, Michael Kroeker, and organized into a centralized knowledge base within the ARIA chatbot. A mixed methods evaluation was conducted utilizing a 5-point Likert scale with three quantitative questions and one open-ended qualitative question. The data was given to the SeniorLine staff, who wanted to …

Freshman 15? Freshman 50?? The Reality Of Daily Life Habits Of A First Year College Student, Gregorio R. Salgado

Student Scholar Symposium Abstracts and Posters

This project presents a personal data tracking study in which I collected daily self-reported metrics over the course of the Spring semester using Excel. The variables tracked include sleep duration, caloric intake, screen time, social media usage, phone checks per day, family communication, and personal spending. The goal of this project is to identify meaningful patterns and correlations between daily habits and personal well-being.

Data was collected through a combination of manual logging and smartphone-generated daily reports. This study explores potential relationships between variables such as sleep duration and social media usage, as well as the association between family communication …

Genetic Analysis Of Triplicated Genes Affecting Sex-Specific Skeletal Deficits In Down Syndrome Model Mice, Kourtney Sloan, Kristina M. Piner, Pathum Randunu Nawarathna Kandedura Arachchige, Charles R. Goodlett, Yann Herault, Gayla R. Olbricht, Joseph M. Wallace, Randall J. Roper

Mathematics and Statistics Faculty Research & Creative Works

Down syndrome (DS) is caused by the triplication of human chromosome 21 (Hsa21), resulting in skeletal insufficiency (low bone mineral density) and altered bone development. DS mouse models recapitulate these deficits, including sexual dimorphism in long bone alterations. Historically, Ts65Dn mice provided much of the insight behind DS-related skeletal deficits with ∼100 trisomic orthologous genes, but there are concerns about the genetic fidelity in this model due to the included triplication of genes not homologous to Hsa21. A new DS model, Ts66Yah, subtracted the non-Hsa21 homologous trisomic genes from Ts65Dn but has not been evaluated for long bone deficits. Comparing …

The Impatience Of Winning: An Analysis Of Time Discounting, Predictive Modeling, And The Nba Draft, Alec R. Plante

Business and Economics Honors Papers

This paper examines whether NBA draft decisions can be better explained by incorporating non-geometric time discounting into a model of general manager decision making. Using a dataset of 285 NBA draft prospects over a 12-year period, the impact of college statistics on Value Over Replacement Player (VORP) is determined, and these impact values are then used to create a “predicted” VORP for the first 4 seasons of each player’s career: a projection of what a general manager might think of a prospect’s future value given their college statistics. Following this, geometric and hyperbolic time discounting models are applied to estimate …

Fossil-Fuels In A Decarbonized Country? Modeling The Drivers Of Icelandic Oil Sales, Inbal Armony

Environmental Studies Honors Projects

Although 100% of Iceland’s electricity comes from renewable energy sources, it still relies on fossil fuels for land transportation, marine transportation, aviation, and some industry. Understanding geographic nuances in oil use is critical to achieving Iceland’s goals of carbon neutrality by 2040. As the island has one primary urban center with two thirds of the population, information is lacking about oil use in non-Capital areas and a gap between state and municipal climate plans. Using newly available data of oil sales at the municipality-level in a Small Area Estimation model, we analyze drivers of oil sales across Icelandic municipalities. We …

Pyspqr: A Python Package For Density Estimation Using Deep Learning, Cameron Eddy, Reetam Majumder

Electrical Engineering and Computer Science Undergraduate Honors Theses

Splines are used for representing complex functions. In statistics, splines can be used for distributional shapes that are difficult to model by traditional parametric approaches. Ramsay (1) uses M-Spline bases to estimate continuous distributions. Semi-Parametric Quantile Regression (SPQR), developed by Xu and Reich (2), models conditional distributions where a neural network is used to estimate the basis function weights that depend on covariates. (3) implements a package for SPQR in R. We build on this by implementing a version of SPQR in Python with PyTorch. By using PyTorch, we can use more sophisticated deep learning architectures than those available in …

Evaluation Of The Effectiveness Of Antihypertensive Therapy Chosen Through Maternal Hemodynamic Profile Analysis, Margaret Weimer

Poster Presentations

In treatment of emergent hypertension, the American College of Obstetricians and Gynecologists (ACOG) recommends both oral labetalol and nifedipine, with no preference shown between the two. These medications have different mechanisms of action. Studies have suggested that consideration of hemodynamic profile may be an effective way to determine medication, but have not considered the Rule of 55, a simple calculation to predict hemodynamic profile.

Goals: 1. Determine if tailoring the antihypertensive to patient’s hemodynamic profile is associated with better control of blood pressure. 2. Determine if the Rule of 55 is an accurate method to determine hemodynamic profile.

Factors Affecting Pedestrian-Vehicle Conflicts: An Empirical Analysis, Christo D. Jamo

Honors Scholar Theses

The number of pedestrian deaths increased by 78% between 2009 and 2023, while other motor vehicle crash deaths increased by 13% in the same period [1]. To identify potential pedestrian safety measures, this study analyzed the effects of location-based demographics, pedestrian phasing type, and other physical infrastructure and behavior variables on the probability of pedestrian-vehicle conflicts at signalized intersections, which is a surrogate measure of crash risk. Data were collected from 55 intersections in Connecticut, and the pedestrian-vehicle interactions were classified by severity based on the Swedish Traffic Conflict Technique: undisturbed passage, potential conflict, minor conflict, or serious conflict. Because …

Feasibility Study Of Transitioning From Thick Plates (0.250”) Mounted On 30-Point Pvc Carriers To Thinner Plate Technologies Mounted On Recyclable Foam And Pet (0.155”) For Post-Print Corrugated, Nathaniel J. Poole

All Theses

In the United States, the most common press configuration for brown-box printing is a 0.280” undercut press. These press configurations have long relied on thick 0.250” plates mounted on 0.030” PVC sheets to print onto corrugated substrates. Each year, around twenty million pounds of waste are produced by the printing industry, through paper waste, plate waste, among other materials. One large factor of that waste is flexographic plate waste, which either ends its life in a landfill or is repurposed into other products. This study establishes a comparison between traditionally used 0.250” plates on 30pt PVC versus 0.155” plates mounted …

Base Running: A Lost Art In Baseball, Ethan York

Departmental Honors & Graduate Capstone Projects

In an era of baseball dominated by home runs and launch angles, the subtle art of baserunning is often overlooked, despite its measurable impact on winning games. Baserunning Runs (BsR) addresses this gap by quantifying the number of runs a player contributes through performance on the basepaths, capturing value beyond traditional metrics like stolen bases. This study constructs multiple regression models that predict BsR for Major League Baseball (MLB) players based on baserunning-related statistics. The primary objective is to examine the association between BsR and key predictors, including stolen bases (SB), extra bases taken (EB), and sprint speed (SS), while …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

Preliminary Sonification Of Enso Using Traditional Javanese Gamelan Scales, Sandy Hs Herho, Rusmawan Suwarman, Nurjanna J. Trilaksono, Iwan P. Anwar, Faiz R. Fajary

Northeast Journal of Complex Systems (NEJCS)

Sonification—the mapping of data to non-speech audio—offers an underexplored channel for representing complex dynamical systems. We treat El Niño-Southern Oscillation (ENSO), a canonical example of low-dimensional climate chaos, as a test case for culturally-situated sonification evaluated through complex systems diagnostics. Using parameter-mapping sonification of the Niño 3.4 sea surface temperature anomaly index (1870–2024), we encode ENSO variability into two traditional Javanese gamelan pentatonic systems (pelog and slendro) across four composition strategies, then analyze the resulting audio as trajectories in a two- dimensional acoustic phase space. Recurrence-based diagnostics, convex hull ge- ometry, and coupling analysis reveal that the sonification …

Efficacy Analysis In Clinical Trials: A Comprehensive Review Of Statistical And Machine Learning Approaches, Dhrubajyoti Ghosh, Samhita Pal

Faculty Articles

Efficacy testing is a cornerstone of clinical trials, ensuring that medical interventions achieve their intended therapeutic effects. Over the decades, a wide range of statistical methodologies have been developed to address the complexities of clinical trial data, including parametric, nonparametric, Bayesian, and machine learning approaches. Parametric methods, such as t-tests, ANOVA, and LMMs, have traditionally been the foundation of efficacy testing due to their efficiency under well-defined assumptions. Nonparametric techniques, including the Friedman test, Brunner-Munzel test, and modern extensions like nparLD, have emerged as robust alternatives, particularly for skewed, ordinal, or non-normal data. Bayesian methodologies have enabled the incorporation of …

Bayesball : A Comprehensive Framework For Predicting Ucl Injury, Brady M. Pinter, Will Best Ph.D.

SPARK Symposium Presentations

Ulnar Collateral Ligament (UCL) reconstruction, commonly referred to as Tommy John Surgery, has seen a significant rise among Major League Baseball (MLB) pitchers, prompting growing interest in identifying the mechanical and performance-based factors that contribute to injury risk. While previous studies have examined these relationships using traditional frequentist approaches separately, this study combines multiple different model techniques to present a broad framework for finding significant predictors of UCL Surgery. These models include Lasso and Ridge Regression,  Principal Component Regression (PCR) , Partial Least Squares Regression (PLS) , Random Forest, Multiple Linear Regression, and a Bayesian Statistical Model. Using these models, …

Saturated Hierarchical Atomic Incremental Learning (Shail): A Behavioral Learning Perspective On Staged Mastery And Saturation, Ernest Fokoue

Articles

We introduce Saturated Hierarchical Atomic Incremental Learning (sHAIL), a learning paradigm in which complex tasks are approached through a sequence of simpler atomic subtasks, each mastered to saturation before progression. The central mechanism is a saturation criterion that detects when learning dynamics enter a plateau region, triggering consolidation and subsequent ascent to a higher level of task complexity. We develop a theoretical framework for sHAIL and show that it naturally gives rise to \emph{staircased convergence}: alternating phases of rapid improvement and genuine plateau. Within each level, classical convergence guarantees apply under standard smoothness conditions, while the hierarchical transitions are driven …

Decorrelation, Diversity, And Emergent Intelligence: The Isomorphism Between Social Insect Colonies And Ensemble Machine Learning, Ernest Fokoue, Gregory Babbitt, Yuval Levental

Articles

Social insect colonies and ensemble machine learning methods represent two of the most successful examples of decentralized information processing in nature and computation respectively. Here we develop a rigorous mathematical framework demonstrating that ant colony decision-making and random forest learning are isomorphic under a common formalism of stochastic ensemble intelligence. We show that the mechanisms by which genetically identical ants achieve functional differentiation— through stochastic response to local cues and positive feedback—map precisely onto the bootstrap aggregation and random feature subsampling that decorrelate decision trees. Using tools from Bayesian inference, multi-armed bandit theory, and statistical learning theory, we prove that …

A General Weighting Theory For Ensemble Learning: Beyond Variance Reduction Via Spectral And Geometric Structure, Ernest Fokoue

Articles

Ensemble learning is traditionally justified as a variance-reduction strategy, explaining its strong performance for unstable predictors such as decision trees. This explanation, however, does not account for ensembles constructed from intrinsically stable estimators-including smoothing splines, kernel ridge regression, Gaussian process regression, and other regularized reproducing kernel Hilbert space (RKHS) methods whose variance is already tightly controlled by regularization and spectral shrinkage. This paper develops a general weighting theory for ensemble learning that moves beyond classical variance-reduction arguments. We formalize ensembles as linear operators acting on a hypothesis space and endow the space of weighting sequences with geometric and spectral constraints. …

Learning Ordinal Geometry: Semantic–Aware Kernels For Ordered Categorical Data, Ernest Fokoue

Articles

Ordinal data arise ubiquitously in survey research, psychology, medicine, economics, and recommender systems, yet kernel methods for such data typically rely on either nominal encodings or arbitrary numeric codings. The former discards order information; the lat- ter imposes a fictitious metric structure. This paper develops a principled framework for kernel design on ordinal scales and introduces a new class of Semantic–Aware Ordinal Ker- nels (SAOK) that simultaneously capture ordinal order and semantic proximity between categories. We begin by formalizing order–preserving embeddings of finite chains and characterizing a broad family of chain distances that are conditionally negative definite. Through Schoen- berg …

Automating Cardiff Model Data Capture In Emergency Departments: Ambient Nlp Integration With Oracle-Cerner Fhir Systems, Simi Augustine, Marco A. Lopez, Jacquelyn Cheun, Chris Papesh

SMU Data Science Review

Violence and overdose events in Las Vegas occur at rates above the national average, with fewer than half of violent injuries reported to law enforcement [2,7]. The Cardiff Model offers a proven framework for standardized data collection and sharing between hospitals and public safety partners, yet many implementations still rely on manual entry. We propose an ambient triage pipeline integrated with Oracle-Cerner electronic health record systems to listen to nurse–patient dialogue, convert speech to text, extract Cardiff fields, and write standards-based FHIR Bundles for analytics. Using SMART on FHIR standards and Cerner Millennium APIs, the study evaluates whether ambient capture …

Using Ensemble Disagreement To Stabilize Conformal Prediction Under Distribution Shift, Patrick D. Murphy

Master's Theses

Semantic segmentation of eelgrass from drone imagery is crucial for coastal habitat monitoring, restoration, and management, as these habitats continue to see rapid changes due to climate change and human influence. However, the reliability of generalizing a deployed classification model relies on both high-accuracy segmentation as well as robust uncertainty quantification that holds up when conditions change over years or locations. Conformal prediction (CP) is a method that converts a classifier's output into prediction sets with a guaranteed average coverage level for in-distribution data. However, the “vanilla” conformal score can often under-cover in hard or out-of-distribution (OOD) regions under drift. …

Selecting Without Replacement From A Population Of Bands Of Serially Connected Objects, James E. Marengo, Dominick Banasik, Joseph Voelkel, David L. Farnsworth

Articles

The sampling procedure from a finite population of objects that are serially attached into bands is described and analyzed. One object is randomly selected and removed at a time, which results in that object’s band being broken into two bands or shortened by one object. The main result gives the probability of choosing an object that is part of a band of serially connected objects of any specified size at each stage of the selection process.

Estimasi Proporsi Pekerja Anak Pulau Maluku & Papua: Pendekatan Small Area Estimation Hierarchical Bayes Distribusi Beta, Apriani Sofiana, Fauzana Afininnas, Fachrol Mochti, Angga Prayoga, Shafira Husna, Nofita Istiana

Jurnal Ekonomi Kependudukan dan Keluarga

Pekerja anak merupakan isu krusial yang memerlukan penanganan segera untuk mendukung pencapaian target pembangunan global. Pengentasan isu ini menuntut ketersediaan data yang akurat hingga wilayah kecil guna mendukung perumusan kebijakan yang tepat sasaran. Penelitian ini bertujuan menduga proporsi pekerja anak usia 5–17 tahun di kabupaten/kota Pulau Maluku dan Papua tahun 2024 menggunakan metode Small Area Estimation (SAE) Hierarchical Bayes (HB) distribusi Beta. Lima variabel penyerta dari PODES dan regsosek dipilih melalui stepwise regression dan dieksplorasi secara spasial. Hasil pemodelan HB Beta Pulau Maluku dan Papua menunjukkan sebagian besar wilayah masih memiliki RSE tinggi. Untuk meningkatkan presisi, dilakukan klasterisasi wilayah sebelum …

Statistical Analysis Of Log Transformation Effectiveness In Air Traffic Movement Forecasting During Covid-19 In South Africa, John Lehlaka Masekoameng

Journal of Aviation Technology and Engineering

This study evaluates the effectiveness of log transformation in enhancing multiple regression models used to forecast air traffic movements (ATMs) in South Africa during the COVID-19 pandemic. Using 60 monthly observations from October 2016 to September 2021, the analysis incorporates variables such as revenue, lockdown levels, COVID-19 metrics, exchange rates, gross domestic product, and population. Two models are compared: one using raw ATMs and another with log-transformed ATMs as the dependent variable.

While the untransformed model shows stronger explanatory power (R² = 0.904, adjusted R² = 0.891) compared to the log-transformed model (R² = 0.772, adjusted R² = 0.741), the …

Distribution Of New Statistics Of Parking Functions And Their Generalizations, Stephan Wagner, Catherine H. Yan, Mei Yin

Mathematics: Faculty Scholarship

In this paper we present new results on the enumeration of parking functions and labeled forests. We introduce new statistics on parking functions, which are then extended to labeled forests via bijective correspondences. We determine the joint distribution of two statistics on parking functions and their counterparts on labeled forests. Our results on labeled forests also serve to explain the mysterious equidistribution between two seemingly unrelated statistics in parking functions recently identified by Stanley and Yin and give an explicit bijection between the two statistics. Extensions of our techniques are discussed, including joint distribution on further refinement of these new …

Comparative Machine Learning Models For Disease Risk Prediction, Mercy Mawusi Agbley

Theses, Dissertations and Capstones

Accurate prediction of disease outcomes is crucial for improving clinical decision-making and enabling early intervention. This study compares the performance of various statistical and machine learning models for clinical risk prediction using two healthcare datasets: diabetic retinopathy and heart disease. The models assessed include Logistic Regression, LASSO, k-Nearest Neighbors (KNN), Support Vector Machines (SVM), Neural Networks, Random Forests, Gradient Boosting Machines (GBM), and a stacked ensemble model. Prior to modeling, datasets were split into train and test sets. Standardization was applied to numeric features whilst categorical features were one-hot encoded. These transformations were later applied to the test set. Principal …

Use Of Tezepelumab For Chronic Rhinosinusitis With Nasal Polyps By Eosinophilic Endotype: Waypoint Post-Hoc Analysis, Shigeharu Fujieda, Nobuyoshi Otori, Joseph K. Han, Tadataka Yabuta, Claudia Chen, Claudio Marchese, Andrews Foster, Sandhia S. Ponnarambil, Yun Chan, Brian J. Lipworth

Department of Otolaryngology (ENT) Faculty Publications

Background

The phase 3 WAYPOINT study (NCT04851964) reported that tezepelumab improved outcomes in patients with chronic rhinosinusitis with nasal polyps (CRSwNP), including nasal polyp size, nasal congestion, and sinonasal symptoms, and reduced the need for surgery and systemic corticosteroids (SCS).

Objective

To evaluate the efficacy and safety of tezepelumab across Japanese Epidemiological Survey of Refractory Eosinophilic Chronic Rhinosinusitis-defined eosinophilic chronic rhinosinusitis (ECRS) subgroups.

Methods

Adults with severe CRSwNP were randomized to tezepelumab 210 mg or placebo every 4 weeks. Coprimary end points were the change from baseline to week 52 in total Nasal Polyp Score and the biweekly mean Nasal …

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 …

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 …