Statistics and Probability Commons^™

Defining Clinically Meaningful Within-Patient Changes In Heart Failure: Jacc Heart Failure Position Statement, Amin Yehya, Rebecca Hahn, Barry Borlaug, Victoria Delgado, Andrew Ambrosy, Ross Arena, Nosheen Reza, Gregory Lewis, Natalie Tapaskar, Salvatore Carbone, Cynthia Chauhan, Mitchell A. Psotka, Norman Stockbridge, James Januzzi, Javed Butler, Jennifer Cowger, Biykem Bozkurt, John Spertus

Department of Medicine Faculty Publications

Heart failure (HF) clinical trials increasingly rely on diverse endpoints beyond mortality, including hospitalizations, imaging, hemodynamic status, biomarkers, functional capacity, and patient-reported outcomes. Although statistically significant differences between treatment groups are commonly reported, interpreting whether these changes are clinically meaningful for individual patients remains challenging. This JACC: Heart Failure position statement proposes a pragmatic framework for defining clinically meaningful within-patient change across commonly used HF outcomes by integrating measurement variability, prognostic associations, and patient-anchored evidence where available. Relative and absolute risk reductions should both inform interpretation of clinical events, while imaging, hemodynamic, biomarker, and functional measures require changes exceeding measurement …

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considered “species of greatest conservation need,” most of the distributional data used to make these designations are outdated, with some dating back over 50 years.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 …

Modeling Healthcare Data With Logistic Quantile And Uniform-Based Mixture Polynomial Distributions, Mohan D. Pant, Aditya Chakraborty, Jovanna A. Tracz

Epidemiology, Biostatistics, & Environmental Health Faculty Publications

Continuous healthcare data often deviate from normality, which can substantially increase the risk of making invalid inferences, given that many inferential statistical procedures rely on normality assumption. To obviate this issue, we propose a new family of non-normal distributions based on a linear combination of the quantile functions of standard logistic and uniform (0, 1) distributions. This new family of non-normal distributions is studied within three different methods: L-moments, conventional moments, and percentiles. Its performance is compared among the three methods in the context of parameter estimation and data modeling. The results of Monte Carlo simulation and bootstrapping techniques indicate …

Nirmatrelvir-Ritonavir Targeting Viral Persistence In Post-Covid-19 Condition (Long Covid) In The Usa (Recover-Vital): A Randomized, Double-Blind, Placebo Controlled, Phase 2 Trial, Lindsey R. Baden, Nirav S. Shah, Sean T. H. Liu, Jonathan Cohen, James May, Andre Kumar, Grace A. Mccomsey, Peter Chen, Michelle Floris-Moore, Nora G. Singer, Inti Fernandez, Alex J. Slandzicki, Zanthia Wiley, Alexandra Kadl, David A. Kaminsky, Harvey Hsu, Tiffany A. Walker, Aluko A. Hope, Luis Ostrosky-Zeichner, Jason D. Goldman, Michael J. Peluso, Thomas F. Patterson, Sairam Parthasarathy, Janet M. Mullington, Paul Bolin Jr., Sarah E. Jolley, Jerry A. Krishnan, Mario Castro, Sally L. Hodder, Priscilla Pemu, Helen Y. Chu, Michael G. Risbano, Maya R. Jerath, Eleftherios Mylonakis, Ryan T. Hurt, Radica Alicic, Nabila S. Azad, Marc A. Sala, Michelle S. Harkins, Jeffrey Parsonnet, Neil Stafford, Philip Robinson, Sabiha Hussain, Xian Qiao, Sophie Two Hawk, Michael Lillestol, Nathan Erdmann, Kelly A. Gebo, Praveen Sudhindra, Joseph Sassine, Gailen D. Marshall, Tulika Chatterjee, Caryn G. Morse, Eyal Kedar, William W. Stringer, Jennifer A. Frontera, Michael Jordon, Caitlin Blaskewicz, Jorge L. Santana, Rachel A. Foot, Cherry Wongtrakool, Matthew William Mccarthy, Alem Mehari, Arch Amon, Alison K. Cohen, Nita Jain, Christine Maughan, Doug Lindsay, Rachel Olson, Samuel Broderick, Pearl Rowe, Sean M. O'Brien, David R. Walt, Bruce D. Levy, Leonard A. Jason, Phillip A. Low, Cyndya A. Shibao, Barry Make, Lucinda Bateman, Susan Redline, David Knopman, Adrian F. Hernandez, Tracy L. Nolen, Craig Reist, Lisa Berdan, Richard Whitley, Kanecia O. Zimmerman, For The Recover-Vital Clinical Trial Group

Department of Medicine Faculty Publications

Background

Post-acute sequelae of SARS-CoV-2 infection, more commonly known as long COVID, has emerged as a major health problem. The pathogenesis of long COVID is unknown, but among the leading hypotheses is viral persistence. We aimed to investigate whether the use of the SARS-CoV-2 antiviral nirmatrelvir-ritonavir improved long COVID symptoms.

Methods

We conducted a double-blind, placebo-controlled, randomised trial involving adults who had developed persistent symptoms (≥12 weeks) associated with three major symptom phenotypes (cognitive, autonomic, or exercise) after acute SARS-CoV-2 infection at 69 US sites. Participants were eligible if they were 18 years or older and had a previous suspected, …

Traveling Waves For A Diffusive Sir Epidemic Model With Delay In The Diffusion Term, William Barker

Faculty Scholarship

This paper investigates the existence of traveling waves in a diffusive SIR model with delay incorporated in the diffusion terms and a nonlinear incidence rate with delay. By employing a cross-iteration scheme and partial monotonicity conditions, we establish that the existence of quasi-upper and lower solutions, along with suitable super and sub-solutions, provides sufficient conditions for the existence of a traveling wavefront. This existence result is obtained via Schauder’s fixed-point theorem. Furthermore, given an appropriate basic reproduction number, the traveling wavefront transitions from the disease-free steady state to the endemic steady state. To illustrate our approach, we explicitly construct super- …

Swimming In Uncertainty: Filling Data Gaps And Providing An Educational Platform For Beach Water Quality At Tybee Island, Georgia, Lukas Roberson

College of Graduate Studies: Theses & Dissertations

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Swimming in beaches water contaminated with high levels of bacteria can make you sick. Current monitoring at the public beaches on Tybee Island consists of weekly monitoring and enumeration of fecal indicator bacteria that takes 24 hours for results. If the number of bacteria exceed regulatory limits, a public health advisory is issued, and affected waters are retested until …

Statistical Quality Control: A Bayesian Framework, Jakia Jaber Tunal

College of Graduate Studies: Theses & Dissertations

In many industries, it is important to assess whether a machine or system is operating within acceptable limits or has gone out of control. This project applies Bayesian statistics to monitor a process over time and detect changes in its behavior. First, initial data are collected to understand the system’s typical performance and to form a starting prior distribution. As new observations arrive over time, the prior is updated through Bayesian inference, combining past information with incoming data. This iterative updating creates a continuous monitoring framework that adapts as more evidence becomes available. When the updated results suggest that the …

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.

Hidden Markov Models For Stock Market Regime Prediction, Meghan Blanch

Electronic Theses & Dissertations (2024 - present)

Hidden Markov Models (HMMs) are a powerful mathematical system used for analyzing time sequences in which the underlying states are unable to be directly observed. This project strives to develop the theory and computation of such models, including deriving the forward and backward variables, the Baum-Welch algorithm, and the Viterbi algorithm. Each of these HMM components are derived and explained to demonstrate the probabilistic principles that allow HMMs to be effective for modeling sequential data.

To demonstrate its practical relevance, the HMM is applied to financial time series. The observable stock market returns tend to be influenced by market regimes …

Entropic Dynamics Approach To The Classical Limit Of Quantum Mechanics: Decoupling Of The Center Of Mass Motion For A Mesoscopic Particle, Fatimah Judayba

Electronic Theses & Dissertations (2024 - present)

In the Entropic Dynamics (ED) approach, quantum mechanics is derived from the principles of entropic inference and information geometry. The ED approach differs from other interpretations by making a clear commitment to distinguishing which variables are ontic (real) and which are epistemic. The classical limit for the center of mass (CM) coordinate is achieved for a large number of particles, M →∞, while Planck’s constant ℏ remains finite. Typically, the emergence of the classical limit requires decoherence through interactions with the external environment. In this work, we investigate whether the classical behavior of the CM coordinate in a mesoscopic system …

Bayesian Modelling On Periodically And Multiple Periodically Correlated Time Series Data, Jie Yao

Electronic Theses & Dissertations (2024 - present)

Time series with multiple periodically correlated (MPC) components present a complex challenge, with relatively limited prior research. Most existing models are designed for simpler periodically correlated (PC) components and often struggle with over-parameterization, optimization issues, and capturing complex PC patterns within a time series. Frequency separation techniques can help preserve the correlation structure of individual PC components, while Bayesian methods can integrate new and prior information to refine beliefs about these components. This study proposes a two-stage approach that combines frequency separation and Bayesian techniques to forecast PC and MPC time series data. This method aims to demonstrate improved effectiveness …

Transformer-Based Language Models For Bitcoin Market Prediction And Interpretation, Erich Gozebina

Masters Theses

"In the context of a Master's thesis in applied mathematics, this work investigates compact transformer-based language models as an instrument for Bitcoin-related predictions and decision support. The work connects three topics: the structure of the Bitcoin system and its data, the mathematical and algorithmic foundations of deep autoregressive transformers, and the design of practical training pipelines for financial applications. On this foundation, a reproducible ETL pipeline for Bitcoin data is developed and two forecasting experiments are conducted with the compact language model nanochat. The first experiment approaches the prediction of next-day price movements through autoregressive next-token generation based on structured …

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 …

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 …

Changepoint Analyses Confirms Global Tropical Cyclone Frequency Decline, Michael Wehner, Thomas Fisher, Norou Diawara, Robert Lund

Mathematics & Statistics Faculty Publications

Changes in tropical cyclone frequencies as the climate warms is a topic of significant current debate [1, 2]. There is no accepted theory of how tropical cyclogenesis might respond to a warmer ocean-atmosphere system as multiple controlling factors exist [3–7]. Anthropogenic warming of surface ocean temperatures due to increased greenhouse gas concentrations [8] increases the potential for tropical cyclogenesis [9–11]; however, realized cyclogenesis also requires an initial local disturbance [12–16] to develop. Most multi-decadal tropical cyclone permitting climate models (i.e. resolutions of 15-50km) exhibit frequency decreases in warmer climates, despite the increase in tropical cyclogenesis potential [17–25]. In this paper, …

Variational Autoencoder Inverse Mapper For Extraction Of Compton Form Factors: Benchmarks And Conditional Learning, Douglas Adams, Md Fayaz Bin Hossen, Joshua Bautista, Gia-Wei Chern, Simonetta Liuti, Marie Boër, Marija Čuić, Michael Engelhardt, Gary R. Goldstein, Huey-Wen Lin, Yaohang Li

Computer Science Faculty Publications

Deeply virtual exclusive scattering processes (DVES) serve as precise probes of nucleon quark and gluon distributions in coordinate space. These distributions are derived from generalized parton distributions (GPDs) via Fourier transform relative to proton momentum transfer. QCD factorization theorems enable DVES to be parameterized by Compton form factors (CFFs), which are convolutions of GPDs with perturbatively calculable kernels. Accurate extraction of CFFs from DVCS, benefiting from interference with the Bethe–Heitler (BH) process and a simpler final state structure, is essential for inferring GPDs. This paper focuses on extracting CFFs from DVCS data using a variational autoencoder inverse mapper (VAIM) and …

Exploring Marshall–Olkin Models Through Bibliometric And Topic Modeling Approaches Uses Latent Dirichlet Allocation (1981-2025): A Study Based On Scopus Data, Humberto Llinás, Brian Llinás, Carlos López, Daniela Nuñez

Computer Science Faculty Publications

The Marshall–Olkin family of distributions has gained increasing attention in fields such as reliability engineering, survival analysis, financial risk modeling, and actuarial science because of its flexibility in modeling dependence among events and its wide range of extensions. Despite its growing relevance, a systematic understanding of how research on Marshall–Olkin models has evolved over time is still limited. This study addresses this gap by combining bibliometric techniques with topic modeling to analyze the structure and evolution of the scientific literature on Marshall–Olkin models. The analysis includes all 266 peer-reviewed publications on Marshall–Olkin models indexed in Scopus between 1981 and 2025. …

The Maxima Method For Identification Of Principal Periodic Components In Time Series Analysis, Megan Di Maio

Electronic Theses & Dissertations (2024 - present)

This dissertation investigates methods for mean estimation in periodically correlated time series, focusing on the Variable Bandpass Periodic Block Bootstrap (VBPBB) and a novel data-driven maxima method. Time series require specific methods because of the temporal correlation in the data. Traditional methods like the General Seasonal Block Bootstrap (GSBB) account for this correlation but often produce wide confidence intervals because they cannot isolate multiple periodicities, allowing noise and other frequencies to interfere with analysis. The VBPBB method addresses this by applying a Kolmogorov-Zurbenko Fourier Transform (KZFT) filter to the data before bootstrapping, which suppresses interfering frequencies and results in narrower, …

Learning Weibull Loss Severity Models From Truncated And Censored Data, Majed Alkhasha

Graduate Studies Theses and Dissertations 2026

In modern actuarial science and risk management, due to various loss control mechanisms, observed severity losses are typically left-truncated at the deductible, right-censored at the policy limit, and scaled by a pre-specified co-insurance factor. This results in two types of actuarial payment random variables: payment-per-payment (PPP) and payment-per-loss (PPL). To learn ground-up Weibull loss severity models from PPP and PPL sample data, we implement two estimation techniques: Maximum Likelihood Estimation (MLE) and the dynamic Method of Trimmed Moments (MTM). MLE is employed to obtain efficient estimates of the Weibull shape and scale parameters. However, MLE may assign unnecessarily large point …

Time Series Decomposition And Forecasting Of Alzheimer’S Disease Mortality Using A Kolmogorov-Zurbenko Filter, Jack D. Farrell

Electronic Theses & Dissertations (2024 - present)

Alzheimer’s disease mortality has substantially risen in recent history, placing a significant burden on public health infrastructure and highlighting the need for improved analytical methods to better understand mortality data patterns and offer reliable predictions. Time series methods often struggle to balance both accuracy and interpretability, which hinders the ability to gather meaningful insights from time series data. To address these limitations, this study applies the Kolmogorov-Zurbenko (KZ) filter to monthly U.S. Alzheimer’s mortality data spanning from 1999 to 2023 and decomposes the series into long-term trend, seasonal, and noise components on a logarithmic scale. Long-term trend accounts for 86.49% …