Statistics and Probability Commons^™

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, …

Implementing A Clustering Framework On Distributional Bee Data, Roheel Nawaz

Research and Creativity Symposium

Understanding spatial patterns in biodiversity is important for identifying how ecological communities are structured across landscapes. Clustering methods provide a useful way to detect non-random species distributions and reveal potential environmental or geographic influences. In this study, we applied a clustering framework to a large long-term bee abundance dataset from the Mid-Atlantic United States to evaluate community structure across regions of Maryland, Delaware, and Washington, D.C.

The dataset included over 1,100 sites and more than 3,000 transects. Because sampling methods were not fully standardized, abundance data were converted to presence/absence and analyzed using the Jaccard index to measure site similarity. …

Factors Associated With Lapses In Care Among People Living With Hiv In South Carolina, Xueying Yang Ph.D., Fanghui Shi, Shujie Chen, Gavi Samuel, Bankole Olatosi Ph.D., Sharon Weissman, Xiaoming Li Ph.D., Jiajia Zhang Ph.D.

Faculty Publications

Utilizing statewide electronic health records (EHR) data, this study aims to assess the factors determining the occurrence of lapses in HIV care among people with HIV (PWH) in South Carolina (SC). All adult (≥ 18 years old) PWH who were diagnosed with HIV between 2006 and 2018 with at least two HIV care encounters and at least 1-year follow-up record were included in the analysis. The outcome, a lapse in care, was defined as a repeated measure of HIV care encounter that occurs over a year following the previous visit. Generalized Estimation Equation models were employed. The study cohort had …

Implementation And Costs Of A Food Insecurity Resource Navigation Program For Primary Care Patients With Diabetes And Hypertension In South Carolina, Deeksha Gupta, Darin Thomas, Stella Coker Watson Self Ph.D., Ms, Edward A. Frongillo Jr. Ph.D., Alain H. Litwin, Joseph A. Ewing, Lynnette Ramos-Gonzalez, Lynnette Ramos-Gonzalez

Faculty Publications

Objective

To examine food insecurity resource navigation program costs and how navigation intensity relates to clinical outcomes, healthcare costs, and quality of life (QOL) for diabetes and/or hypertension patients.

Methods

This retrospective study included patients receiving resource navigation (July 12, 2021-December 31, 2022 with twelve-month follow-up) across three primary care practices in South Carolina's largest health system. Participants were 18+ years old (from electronic medical records/Epic), had food insecurity (from Hunger Vital Sign™), and diabetes and/or hypertension (from Epic registries). Matched controls came from food insecurity screening-only practices. Patients in each group (n= 219) had diabetes (9.13%), hypertension …

Information Theory Analysis Of The Solar Wind Magnetic Structures For Space Weather Prediction, Katherine Holland

Doctoral Dissertations and Master's Theses

Forecasting space weather at Earth is highly complicated, because of the limited measurements of the dynamic processes in the Sun that span multiple temporal, spatial, and energy-scales. The solar wind is a highly structured, multi-scale, evolving plasma and consists of coronal mass ejections (CMEs), stream interaction regions (SIRs), expanding flux tubes (Borovsky, 2008), and interplanetary magnetic field (IMF) discontinuities and fluctuations. The aim of this research is to improve our understanding of the evolution and dissipation of different scale-size solar wind magnetic structures as they move from the Sun-Earth Lagrange point 1 (L1) to Earth's bow shock and, ultimately, to …

Traveling Waves In Reaction-Diffusion Equations With Delay In The Diffusion Term, William Barker, Van Minh Nguyen

Faculty Scholarship

We investigate the existence of traveling wave solutions for the reaction–diffusion equation ∂u(x,t)∂t=Δu(x,t−τ1)+f(u(x,t),u(x,t−τ2)), where τ1, τ2 > 0. This model is motivated by ecological applications in which migration rates incorporate historical effects and reproduction/death processes are subject to time delays at a given location. To address such systems under standard monotonicity assumptions, we extend the classical monotone iteration method. A key step involves a thorough investigation of the Green function associated with the functional equation x″(t)−ax′(t+r)−bx(t+r)=f(t), where a ≠ 0 and b > 0. Building on the resulting framework, we construct quasi-upper and lower solutions for the Belousov–Zhabotinski equations, thereby demonstrating the …

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 …

No Intelligence Without Statistics: The Invisible Backbone Of Artificial Intelligence, Ernest Fokoue

Articles

The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars—Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification—demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the …

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. …

On The Scientific Stature Of Data Science: The Epistemological Unicorn, Ernest Fokoue

Articles

Data Science has ignited unprecedented academic, industrial, and pedagogical fervor, yet its status as a \textit{science} in the classical sense---comparable to physics or biology---remains profoundly unsettled. This article interrogates the epistemological foundations of Data Science by examining its hybrid theoretical lineage, from the Universal Approximation Theorem to the No-Free-Lunch Theorems, with special emphasis on the fundamental Bayesian optimality results for both regression and classification. We argue that Data Science is in a vigorous \textit{gestational period}, characterized not by an absence of principles but by a creative tension between empirical pragmatism and deep mathematical theory. The Cross-Validation score emerges as the …

On Fibonacci Ensembles: An Alternative Approach To Ensemble Learning Inspired By The Timeless Architecture Of The Golden Ratio, Ernest Fokoue

Articles

Nature rarely reveals her secrets bluntly, yet in the Fibonacci sequence she grants us a glimpse of her quiet architecture of growth, harmony, and recursive stability \citep{Koshy2001Fibonacci, Livio2002GoldenRatio}. From spiral galaxies to the unfolding of leaves, this humble sequence reflects a universal grammar of balance. In this work, we introduce \emph{Fibonacci Ensembles}, a mathematically principled yet philosophically inspired framework for ensemble learning that complements and extends classical aggregation schemes such as bagging, boosting, and random forests \citep{Breiman1996Bagging, Breiman2001RandomForests, Friedman2001GBM, Zhou2012Ensemble, HastieTibshiraniFriedman2009ESL}. Two intertwined formulations unfold: (1) the use of normalized Fibonacci weights -- tempered through orthogonalization and Rao--Blackwell optimization -- …

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 …

Measuring Market Risk Through Entropic Var, Dragomir Nedeltchev, Tsvetelin Zaevski

Mathematical Modelling and Numerical Simulation with Applications

The article aims to measure the market risk beyond the basic risk measures like the Value-at-Risk (VaR) and the Expected Shortfall (ES). The Entropic Value-at-Risk is selected among the available measures based on its advantages -- it is the coherent upper bound of the VaR and ES. This risk measure is applied to the classical Black-Scholes model as well as to some more realistic ones, such as the exponential tempered stable model (the log-returns are presented by a tempered stable L\'evy process), the stochastic volatility model of Heston, its jump extension of Bates, and another stochastic volatility model but with …

The Blurred Boundaries Of Care: A Qualitative Analysis Of Nurse-Doula Role Conflict, Curisa Mae Tucker Phd, Rn, Maria Mcclam, Kelly Russin Dnp, Rnc-Ob, Chse, Nansi Boghossian, Rachel Gulczinski, Lauren Workman

Faculty Publications

Introduction:

Methods:

Association Between The Dietary Index For Gut Microbiota (Di-Gm) And Colorectal Cancer In The Plco Cohort, Bezawit E. Kase, Angela D. Liese Ph.D., Jiajia Zhang Ph.D., Elizabeth Angela Murphy, Susan E. Steck Phd, Mph, Rd

Faculty Publications

Objectives: The study aimed to examine the association between a dietary index for gut microbiota (DI-GM) and the risk of incident colorectal cancer (CRC). Clarifying the role of diet-induced alterations in the composition and function of gut microbiota on the development of CRC can contribute to prevention efforts. Methods: Participants from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening trial enrolled in the intervention arm and who completed baseline assessments were included in the analysis (n = 55,685). The DI-GM is a literature-derived index used to score diet quality in terms of maintaining healthy gut microbiota. A time-dependent Cox model …

Association Between The Dietary Index For Gut Microbiota (Di-Gm) And Colorectal Cancer In The Plco Cohort, Bezawit E. Kase, Angela D. Liese, Jiajia Zhang, Elizabeth Angela Murphy, Susan E. Steck

Faculty Publications

Objectives: The study aimed to examine the association between a dietary index for gut microbiota (DI-GM) and the risk of incident colorectal cancer (CRC). Clarifying the role of diet-induced alterations in the composition and function of gut microbiota on the development of CRC can contribute to prevention efforts. Methods: Participants from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening trial enrolled in the intervention arm and who completed baseline assessments were included in the analysis (n = 55,685). The DI-GM is a literature-derived index used to score diet quality in terms of maintaining healthy gut microbiota. A time-dependent Cox model …

Dietary Inflammatory Index And Objective Disease Activity In Ibd: No Association Found, Rúbia Moresi Vianna De Oliveira, Ana Carolina Junqueira Vasques, Stefhani Andrioli Romero, Nitin Shivappa Mbbs, Mph, Ph.D., Michael David Wirth, James Hébert Scd, Glaucia Fernanda Soares Ruppert Reis, Cristiane Kibune Nagasako

Faculty Publications

Background

Inflammatory Bowel Disease (IBD) involves genetic and environmental factors, but the relationship between disease activity, adiposity, and diet remains unclear.

Objective

To investigate the association between endoscopic/radiological activity of IBD, body adiposity, and the Dietary Inflammatory Index with or without adjustment for energy density (E-DII or DII).

Method

An observational, cross-sectional study was carried out. Endoscopic activity was defined by an endoscopic Mayo score >2, Crohn’s Disease Endoscopic Index of Severity (CDEIS) > 5, and/or the presence of a deep ulcer in any intestinal segment. Body adiposity was estimated using the body mass index, waist circumference, and waist-hip ratio (WHR). …

Circulating Levels Of Insulin-Like Growth Factor I (Igf-I) And Risk Of Multiple Myeloma: An Observational And Mendelian Randomisation Study, Yolanda Benavente, Sara Hermosa, Nikos Papadimitriou, Alyssa I. Clay-Gilmour Ph.D., Elizabeth E. Brown, Jonathan N. Hofmann, Nathaniel Rothman, Qin Lan, Sonja I. Berndt, Demetrius Albanes, Mark Purdue, Mitchell J. Machiela, Stephen J. Chanock, Parveen Bhatti, Wendy Cozen, Aaron Norman, Susan L. Slager, James R. Cerhan, Vincent Rajkumar, Et. Al.

Faculty Publications

No abstract provided.