Statistics and Probability Commons^™

Likelihood-Based Inference For Random Networks With Changepoints, Daniel Cirkovic, Tiandong Wang, Xianyang Zhang

Mathematical and Statistical Science Faculty Research and Publications

Generative, temporal network models play an important role in analyzing the dependence structure and evolution patterns of complex networks. Due to the complicated nature of real network data, it is often naive to assume that the underlying data-generative mechanism itself is invariant with time. Such observation leads to the study of changepoints or sudden shifts in the distributional structure of the evolving network. In this paper, we propose a likelihood-based methodology to detect changepoints in undirected, affine preferential attachment networks where, upon introduction, a new node selects one old to attach to with probability proportional to its degree. In particular, …

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 …

Two-Stage Response-Adaptive Randomization Designs For Multi-Arm Trials With Normal Outcome, Tanjin Tamanna Happy

UNF Graduate Theses and Dissertations

This study focuses on improving how clinical trials compare new treatments with a standard treatment, when the response is quantitative (normally distributed). In a common two-stage design, several new treatments are first evaluated, and the best-performing one is selected if it appears better than the standard. In the second stage, this selected treatment is compared again with the standard using additional data to confirm its effectiveness. This approach is known to be efficient in terms of accuracy and sample size savings. We extend this design by introducing an adaptive method for assigning patients to treatments in the second stage. Instead …

Inferential Statistics For Industrial Organizational Psychologists: A Practical Guide For Testing Hypotheses Using R, Caitlin Lapine

Open Touro Created

2026

This text aims to provide a practical guide for students in industrial organizational psychology or related fields to complete inferential statistics using R open-source programming language. It provides information about when to use particular statistical analyses and how to perform those with statistical software.

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. …

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 …

Multivariate Quantile Autoregression-Mixed Data Sampling (Mvqar-Midas) Modeling Of Cost Of Living And Supply Chain Dynamics In Canada., Patrick Gbolonyo

Theses and Dissertations (Comprehensive)

In recent years, the rising cost of living as a result of persistent inflationary pressures, disruptions in the global supply chains, and changes in the macroeconomic landscape has become a critical topic of discussion. To address this, we move beyond a mean-based framework and employ a quantile regression approach. This allows the persistence of each series and the transmis- sion of shocks between the Consumer Price Index (CPI) (the total CPI which is a percentage change over the past 12 months), the Interest Rate (IR)(the target for the overnight rate), the New Housing Price Index (NHPI), and high-frequency supply chain …

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

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, …

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% …

Spectral Analysis Of Traffic Accidents In New York's Capital Region, Michael Barr

Electronic Theses & Dissertations (2024 - present)

In this paper we estimate the spectral density of traffic accident events in the Capital Distict, NY area using a band-pass filter known as the Kolmogorov-Zurbenko Fourier Transform (KZFT). The source data is provided by Moosavi, et al. (2019) and originally captured from various public entities and sensors in the road network. Spectral density estimation with KZFT suppresses noise to reveal the constituent frequencies embedded in the noisy signal. Signal reconstruction based on KZFT produces an approximate weekly accident arrivals for this noisy signal, or in other words a pattern which is proportionate to the event expectation viewed over a …

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 …

Entropic Foundation Of Finance And Physics: Securities Price Dynamics And Quantum Theory, Mohammad Abedi

Electronic Theses & Dissertations (2024 - present)

In many scientific and financial contexts, we must reason and make predictions under conditions of incomplete information. This dissertation develops Entropic Dynamics (ED) as a unified framework for deriving dynamical laws directly from principles of inference. Within this approach, probability distributions represent states of knowledge, and their evolution is determined through entropy maximization subject to relevant constraints. This leads to a novel concept of entropic time and a formulation of dynamics as an inferential process. In this talk, I will present how ED provides a common foundation across multiple domains. In physics, quantum dynamics for particles and scalar fields in …

Cross-Temporal Statistical Approaches For Evaluating Predictor-Outcome Relationships, Jeff Joseph

Dartmouth College Ph.D Dissertations

Central auditory function is linked with cognitive deficits, but few research projects use existing statistical approaches or develop new ones to forecast cognitive deficits using the results of central auditory tests. To address this limitation, we use a series of statistical learning frameworks for predicting a child’s cognitive abilities based on his/her central auditory performances and demographic factors. Two key challenges exist. First, children may start the study at a time when they are unable to perform the central auditory tests or cognitive tests. Second, cognitive performance is age-dependent, particularly in the early formative years of childhood and adolescence. To …

A Comparative Evaluation Of Data Imbalance Handling Techniques In Machine Learning Models For One-Year Mortality Prediction In Liver Cirrhosis, Sumiya Hasan Trisha

UNF Graduate Theses and Dissertations

Liver cirrhosis is associated with substantial morbidity and mortality, making one-year mortality prediction a clinically relevant problem. Using a liver cirrhosis dataset as the motivating application, this thesis evaluates five machine learning classifiers—Logistic Regression, Random Forest, XGBoost, LightGBM, and CatBoost—under five class-imbalance handling strategies: Baseline learning, Random Oversampling, SMOTE-NC, ADASYN, and Cost-Sensitive Learning. Hyperparameter tuning was conducted using randomized search, and predictive performance was assessed over 200 iterations of Monte Carlo Cross-Validation using Accuracy, Precision, Recall, Fl-score, and ROC-AUC.

The results suggest that imbalance-handling strategies can materially affect predictive performance, particularly recall. Because the outcome of interest is death within …

Ridit-Based Adaptive Allocation In Two-Stage Clinical Trials With Binary Outcomes, Dewan Fahim

UNF Graduate Theses and Dissertations

This study explores better ways to assign patients to treatments in clinical trials with binary outcomes, such as success or failure. Adaptive methods are used to learn from early results and adjust treatment assignments during the trial, helping more patients receive better performing treatments while maintaining reliable conclusions. We focus on trials comparing multiple treatments using a two-stage design. In the first stage, several treatments are tested to identify the most promising one; in the second stage, that treatment is compared with a control. Unlike traditional equal assignment, we use adaptive allocation in the second stage to make better use …

A Comparative Study Of Classification Methods For Healthcare Analytics, Xueting Zhao

UNF Graduate Theses and Dissertations

This thesis presents a comparative study of logistic regression, Linear Discriminant Analy- sis (LDA), and Quadratic Discriminant Analysis (QDA) for binary classification in healthcare analytics, integrating theoretical derivation, simulation, and real-data application. A facto- rial simulation study crosses the covariance structure (equal vs. unequal), predictor correla- tion (ρ ∈ {0, 0.5, 0.9}), dimensionality (p ∈ {2, 5, 10}) and sample size (n ∈ {50, 100, 200}) across 54 scenarios with 1,000 Monte Carlo replicates each. Three main findings emerge. Logistic regression and LDA are nearly interchangeable when the assumption of equal-covariance holds. QDA achieves substantially better discrimi- nation when class-specific …

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 …

Performance Of Numerical Methods Applied To The Black–Scholes Model, Scott Cameron Williams

UNF Graduate Theses and Dissertations

We compare five numerical approaches for approximating solutions to the Black–Scholes partial differential equation for pricing European call options: FTCS, BTCS, Crank– Nicolson, Monte Carlo simulation, and a physics–informed neural network (PINN). These methods span finite difference techniques, probabilistic simulation, and machine learning. Performance is evaluated based on computational efficiency and accuracy relative to the analytical Black–Scholes solution.

Among the methods, Crank–Nicolson and the PINN demonstrated the strongest overall performance. Crank–Nicolson achieved the highest accuracy but exhibited increased runtime as the number of underlying stock price grid points grew. In contrast, the PINN produced slightly less accurate results but with …

Variance Shrinkage In Dunnett-Type Multiple Comparisons With Missing Data, Md Habibullah

UNF Graduate Theses and Dissertations

Dunnett’s procedure is widely used for comparing multiple treatments with a control, but its application becomes challenging in the presence of missing data and multiple com- parisons. An improved Dunnett-type procedure addresses this by using multiple imputation under Rubin’s framework and constructing unified confidence intervals based on a multi- variate t distribution, allowing valid simultaneous inference while controlling the family-wise error rate (FWER). This work further extends the method by incorporating shrinkage-based variance estimation. Specifically, individual group variances are shrunk toward a common value to improve stability. This approach is particularly effective when group variances are similar or moderately different, …

Body Mass Index Has No Impact On Complications And Mortality For Patients With Stage Iv Pancreatic Ductal Adenocarcinoma, Ren Bryant, Hannah Darnell, Megan Hall, Kelsey N. Karnik, Kristen J. Mcquerry, Ruben R. Plentz

Biostatistics Faculty Publications

Background: Pancreatic ductal adenocarcinoma (PDAC) is one of the leading causes of United States (USA) cancer death. Overweight and obesity developing into a growing global medical and socio-economic problem, affecting approximately 42% of adults in the USA population. The aim of our analysis was to evaluate the influence of overweight and obesity on complications and clinical outcome in patients with stage IV PDAC.

Methods: We retrospectively reviewed electronic health records of patients diagnosed with stage IV PDAC (n=162) who followed with the University of Kentucky from January 2017–October 2024. Comparisons were based on the body mass index (BMI): low BMI …

The Excess Path Length Distribution: A Stochastic Model For Sample-Based Path Planners, Chaz B. Cornwall

Dissertations, Master's Theses and Master's Reports

Through random sampling, sample-based path planners enable autonomous agents to quickly find paths without human intervention. However, due to the paths' randomness, sample-based path planners currently require additional verification, partially nullifying agents' ability to act autonomously. I set out to characterize this uncertainty so humans know what to expect from these path planners and know how to alter the path planner to desired specifications. To ensure the results are theoretical as well as practical, I first create a stochastic model of path length uncertainty using the trade-off between sampling time and optimality. By leveraging this model, my proposed algorithm reduces …

Computational And Ai Frameworks For Identifying Key Regulatory Genes And Their Target Genes In Plants And Humans, Md Khairul Islam

Dissertations, Master's Theses and Master's Reports

This dissertation presents computational and AI-driven frameworks for identifying key regulatory genes and their downstream targets across plant and human biological systems. Three studies address distinct challenges in genomic regulation using advanced machine learning and bioinformatics approaches.

The first study introduces DyGAF (Dynamic Gene Attention Focus), a dual-attention transformer framework that identifies and ranks disease-relevant biomarker genes by simultaneously modeling independent molecular responses and interdependent regulatory network behavior. Two attention models provide complementary perspectives on gene importance and are fused through a novel combination metric. Applied to COVID-19 nasopharyngeal swab profiles, the attention-weighted representations achieved 94.23% classification accuracy, high sensitivity, …

Bayesian Analysis Of Nominal Outcomes With Missing Values Using Multinomial And Multivariate Multinomial Probit Models, Suwash Silwal

Dissertations, Master's Theses and Master's Reports

Nominal outcomes frequently arise in health sciences, transportation, economics, market research, and related fields. These data often contain missing values, while longitudinal and panel studies generate multiple correlated nominal responses. Bayesian estimation of multinomial probit (MNP) and multivariate multinomial probit (MMNP) models provides a flexible framework for analyzing such data but remains computationally challenging due to high-dimensional likelihood integration, restrictive covariance identification constraints, and poor mixing of Markov chain Monte Carlo (MCMC) algorithms, particularly in the presence of missing data. This dissertation develops parameter-expanded data augmentation (PX-DA) methods for MNP and MMNP models with missing nominal outcomes by incorporating parameter …

Using Automotive Lidar To Reduce The Energy Consumption Of An Ego Autonomous Vehicle, Logan P. Schexnaydre

Dissertations, Master's Theses and Master's Reports

There is significant potential to reduce the energy consumption of the transportation sector through autonomous vehicles. Prior work on autonomous vehicle energy efficiency focuses on the whole system or the control subsystem. Yet, the sensing and processing components, which have direct and indirect effects on net energy use, are less explored. This dissertation fills this gap by modeling and evaluating these effects for lidar sensors, which provide high-resolution spatial data at the cost of high power and processing demands. I apply lidar to the energy-saving tasks of automated vehicle following and road surface profiling. For automated vehicle following, I model …

High Algal Biomass Is Decoupled From Metabolism In The Gallatin River, Cora Mae Steinbach

Graduate Student Theses, Dissertations, & Professional Papers

Assessing eutrophication in rivers is difficult compared to lakes and coastal waters, because most algal biomass occurs on the riverbed and flows interact and co-vary with production (Biggs and Close, 1989; Bernhardt et al., 2018). Riverine eutrophication is typically assessed using algal biomass and water column nutrients (U.S. Environmental Protection Agency, 2000), but biomass is highly variable and labor-intensive to measure, while nutrient concentrations often underestimate enrichment due to rapid biological uptake (Dodds and Smith, 2016). Reach-scale river metabolism can help evaluate long-term functional change in rivers recovering from nutrient enrichment (Arroita et al., 2019; Jankowski et al., 2021; Diamond …