Statistics and Probability Commons^™

The Presence Of Outer Giant Planets And Their Role In Inner Planet Formation With And Without Their Influence, Mateo E. Guerra Toro

Graduate Theses/Dissertations

We performed dynamical simulations of the giant impact phase of planet formation to investigate the formation of inner terrestrial planets under the influence of 4 solar system-like outer giant planets. We developed a new code using the N-body simulation suite REBOUND and REBOUNDx (Rein et al. (2019) and Tamayo et al. (2019)) to simulate 2 stages of planetary formation: a residual gaseous protoplanetary disk phase and subsequent dynamical evolution after the disk photoevaporates. The initial conditions for the inner planetary embryos were taken by Morrison et al. (2020) based on a range of solid surface densities that produced Super-Earth terrestrial …

Applications Of Bayesian Functional Data Analysis, Zhexuan Yang

Graduate Research Theses & Dissertations

Functional Data Analysis (FDA) is a statistical approach used to analyze data that vary across a domain, such as curves or functions. This dissertation investigates Bayesian Functional Data Analysis (BFDA) through three applications. First, we explore the use of BFDA in outcome-dependent follow-up (ODFL) studies. After conducting simulation studies, we apply our model to cardiotoxicity and kidney function data. Second, we extend BFDA to genetic data by modeling DNA methylation levels with a three-parameter skew-normal distribution and an alpha-skew generalized normal distribution. This study also introduces a novel Multistage Markov Chain Monte Carlo (MMCMC) method with the goal of identifying …

Covariance Matrix Forecasting Of Equity Portfolios, Michael Nebor

Graduate Research Theses & Dissertations

This dissertation consists of two papers. The first paper introduces DCC-SVR, a hybrid Dynamic Conditional Correlation (DCC) and Support Vector Regression (SVR) method of forecasting the covariance matrix. This paper shows that DCC-SVR is able to outperform the traditional methods of DCC and rolling historical on multiple data sets. Performance is shown for both standard GARCH and GJR-GARCH methods. This paper also analyzes performance when dimensions are increased to 49 dimensions and when an application using equal weighted portfolio allocation is used.

The second paper introduces a covariance matrix forecasting method based on copula-GARCH simulated returns. The accuracy of this …

Efficient Algorithms For Nearest Correlation Matrix Computation With Missing Data, Ibrahim Eniola Oyeyinka

Graduate Research Theses & Dissertations

This thesis investigates efficient algorithms for computing the Nearest Correlation Matrix (NCM) under incomplete financial data. Correlation matrices are vital in portfolio optimization and risk management, yet empirical estimates often violate symmetry, positive semidefiniteness, and unit diagonal conditions due to missing observations. Two projection-based methods are analyzed: the Modified Alternating Projections (MAP) and Anderson Acceleration (AA). Theoretical analysis using convex optimization and normal cone characterization supports numerical evaluation on synthetic and real-world stock-return matrices (550×550, 2020–2025). Missing data are modeled through Missing Completely at Random (MCAR) and Not Missing at Random (NMAR) mechanisms. The results show that AA converges faster …

A Modern Optimization Approach With Data-Driven Analytical Modeling For The Healthcare Business Segment (Hbs) From The S&P 500, Aditya Chakraborty, Chris Tsokos

Epidemiology, Biostatistics, & Environmental Health Faculty Publications

Introduction: The S&P consists of eleven business segments, which are classified according to the type of industry. The current study focuses on developing a non-linear analytical model for the Healthcare Business Segment (HBS) of the S&P 500, as a function of different economic & financial indicators. Materials and Methods: The analytical model used six financial indicators together with four economic indicators to predict the weekly average closing price (WCP) of HBS stocks. Johnson’s SB transformation corrected skewness, while desirability-based optimization identified indicator values maximizing WCP. The model’s performance and generalizability were validated through repeated 10-fold cross-validation. Results: All attributable contributors …

Pediatric Cancer Incidence, Temporal Trends, And Mortality In The United States By Health Disparities Indicators, Seer (1973-2014), Prachi P. Chavan, Laurens Holmes Jr.

Epidemiology, Biostatistics, & Environmental Health Faculty Publications

Background: Pediatric cancer incidence has been increasing in the United States, despite improvement in pediatric cancer survival. This steady increase in incidence trends is not completely understood but maybe associated with social and environmental factors. In this study we aimed to assess the cumulative incidence, temporal trends, and mortality rates in pediatric cancer. Additionally, we examined sub-group variability in both incidence and mortality rates. Methods: Data from Surveillance, Epidemiology, and End Results (SEER) −18 from 1973–2014 were used for the purpose of analysis in this study. Age-adjusted incidence rates were used to assess temporal trends in cancer among children aged < 1–19 years. Univariable and multivariable binomial regression models were used to examine the association between race and cancer mortality while adjusting for potential confounders. Results: There were 92,594 cancer diagnoses during this period. White children comprised 74,758, (80.7%), black children 10,030, (10.8%), and other races 6648, (7.2%). Overall the age-adjusted cumulative incidence was slightly higher among white children (16.4%) than black children (12.4%) and other (13.0%). Children aged 15–19 years and those in metropolitan regions were more likely to be diagnosed with pediatric cancer. Relative to females, males were 16% more likely to die from the disease [adjusted Risk Ratio (aRR): 1.16, 95% Confidence Interval (CI): 1.09–1.22]. Additionally, compared to white children, black children had higher mortality rates [(aRR): 1.37, 99% CI: 1.23–1.52]. Conclusions: There is an increasing trend in pediatric cancer incidence; while white children have the highest incidence, black children and males indicated a survival disadvantage, indicative of racial and sex variability in overall pediatric cancer in the United States.

Estimating The Gender Wage Gap: A Comparative Analysis Of Different Estimators, Xinran Zhang

Mathematics, Statistics, and Computer Science Honors Projects

The gender wage gap between males and females has been well studied by labor economists. We take a multi-prong approach to evaluate three estimators —a regression-imputation estimator, a weighting estimator, and a doubly robust estimator—in estimating the gender wage gap. Using the Panel Study of Income Dynamics, we conduct an empirical study of the estimators’ performances. In a simulation study, we evaluate the properties of estimators and study whether bootstrapping is an appropriate measure of the uncertainty of each estimator. The findings show that while the estimators provide different results, the doubly robust estimator provides reliable and consistent results under …

Action This Day: The Mathematics And Machinations That Bested The German Enigma, Jonah Weinbaum

Dartmouth College Master’s Theses

This thesis presents a comprehensive and chronological overview of cryptographic techniques designed to break Enigma, beginning in 1932 and culminating in the creation of the Turing-Welchman Bombe. We discuss the mathematical theory and electromechanical implements used to decode one of history's greatest ciphers.

Reexamining the Bombe through the lens of modern group theory, we critique Alan Turing's estimation of the number of "stops" that the Bombe produces for various plaintext-ciphertext pairing structures. To address its limitations, we introduce a new framework for estimating the number of stops by extending John Dixon's theorem concerning the probability that uniformly distributed elements of …

Food Insecurity Among Graduate Students At The University Of Alabama At Birmingham, Amy Elizabeth Callahan

All ETDs from UAB

College food insecurity (FI) has grown steadily as a field of research over the past fifteen years. Existing research primarily has demonstrated that FI is a persistent problem with various risk factors and myriad potential impacts on students, though graduate students are largely understudied in favor of undergraduate and aggregated student populations. Given the unique circumstances graduate students face, as well as expected demographic differences such as age and household characteristics, this is a serious gap in the literature. This dissertation aims to investigate graduate student food insecurity in the United States, and particularly at the University of Alabama at …

Bayesian Networks For Safety-Critical Systems, Joseph Mietkiewicz

Theses

This thesis addresses a operational challenge in modern industrial operations: the increasing complexity of systems and the consequent cognitive burden on operators. As industrial technologies advance, the human-computer interface has become the primary conduit for information flow, playing a pivotal role in operational decision-making. However, the proliferation of data often leads to information overload, potentially compromising rather than enhancing operator performance. This research explores an approach to this pressing issue through the application of Bayesian networks as decision support systems in safety- critical scenarios. Our study employs a multi-faceted approach, combining theoretical modeling with empirical testing. Through collaboration with industry …

Optimal Data Splitting Methods, Sujay Mudalgi

Theses and Dissertations

In predictive modeling, effective data splitting is crucial for creating statistically representative training and validation sets. The state-of-the-art data splitting methods are based on minimizing the energy distance between the split subsets. However, there are a number of limitations in the existing methods, which this dissertation aims to address. First, the existing methods were computationally inefficient. Thus, Chapter 2 proposes a method to scale up these approaches for big data. Here, we introduce scalable Twinning (s-Twinning), which significantly improves the execution speed of data splitting without sacrificing accuracy. Second, the existing methods did not consider the predictive relationship in the …

Machine Learning Models Leveraging Patient-Similarity And Clinical Temporality For Disease Prognoses, Ahmad F. Al Musawi

Theses and Dissertations

Electronic Health Records (EHRs) constitute a comprehensive and high-dimensional repository of clinical data, encompassing a wide array of patient-level information such as diagnoses, procedures, medications, laboratory results, and unstructured clinical narratives. These data hold immense potential for advancing predictive modeling in healthcare, including tasks such as disease progression modeling, hospital readmission prediction, and length of stay (LoS) estimation. However, the intrinsic complexity of EHR data—manifested in its heterogeneity, sparsity, and temporal dynamics—poses significant analytical challenges that limit the generalizability and interpretability of conventional machine learning models. Recent methodological advancements in deep learning and graph-based learning, particularly Graph Neural Networks (GNNs), …

An Adaptive Method For Covariate Balancing In Block Randomized Clinical Trials, Ren Rasnick

Theses and Dissertations

Clinical trials are randomized in part to limit allocation bias, but also to ensure comparability between treatment arms for a baseline variable of concern. Comparable with regard to a baseline variable of concern is necessary for the validity of statistical methods. However, comparability is not guaranteed for trials of any size and is even more likely in trials with < 200 total participants. We propose a new method for adapting the allocation of participants in a sequentially allocated two-armed study with a small sample size to better ensure comparability.

The proposed method calculates the expected final imbalance (lack of comparability) based on the current participant values. Unlike several other methods, our method ensures the final desired sample size for each treatment arm, utilizes the expected final imbalance, increases comparability between …

Climate Migration And Urban Survival: Evidence From Chittagong’S Slums, Mohammad Nur Nobi

Graduate Research Theses & Dissertations

This study examines the impact of climate change on rural-to-urban migration in Chittagong, Bangladesh. Based on a primary survey of 400 respondents across 35 slums in the country's second-largest city, the analysis employs two estimation methods: a multinomial logit model to assess the influence of climate-related factors on migration decisions, and a logit model to evaluate the impact of migration on the living conditions of migrants. The results show that individuals involved in ‘agriculture and daily labor’ are most likely to migrate. Compared to the base category (‘Other Reasons’) for migration, the odds ratios for ‘floods’, ‘droughts’, and ‘better job …

Effect Of Universal Health Coverage On Neonatal Mortality Rate In Sub-Saharan Africa: Addressing Missing Data In Health Indicators, Elizabeth Nalule Arihoona

Graduate Research Theses & Dissertations

This study utilizes two mixed-effects models to examine the effect of Universal Health Coverage on Neonatal Mortality Rate (NMR) in 30 countries of Sub-Saharan Africa from 2000-2019 while addressing the missing data in health indicators. Using natural cubic spline interpolation, I impute the missing values in the health coverage indices to preserve the location- specific trends of the data. Findings indicate that among the health Coverage indices, only Index1, which directly relates to coverage of maternal, newborn and child health services is significantly associated with reduced NMR. While higher Current Health Expenditure is associated with reduced NMR, a higher share …

Unlocking The Secrets Of High-Frequency Financial Data: Innovative Approaches To Modeling And Analysis, Lu Zhang

Graduate Research Theses & Dissertations

High-frequency trading (HFT) has emerged as a pivotal innovation in modern financial markets, characterized by rapid, data-driven decision-making processes that capitalize on granular, time-stamped market data. This dissertation examines the predictability of intraday stock price movements during the final 30 minutes of U.S. trading, employing a Bayesian regression model with Student-t error terms to address the limitations of traditional Gaussian-based methods. The analysis reveals a decline in established predictors and the emergence of new dynamics, such as post-Federal Reserve "tug-of-war" effects. The research further advances high-frequency financial modeling by introducing a comprehensive data engineering pipeline and applying cutting-edge deep learning …

Linking Empirical Data And Numerical Simulation To Characterize Dynamic Fire Behavior Associated With Interacting Firelines, Marta Sergeevna Jerebets

Graduate Student Theses, Dissertations, & Professional Papers

Understanding fuel pattern-fire process relationships is key for predicting fire behavior and effects with follow-on benefits to proactive fire management and model validation. To characterize dynamic fire behavior, this thesis leverages empirical data and numerical simulation through two complementary studies.

In the first study, longwave thermal sensors aboard unmanned aerial systems (UAS) were used to capture fine-scale fire behavior in two experimental grass burns. A novel paired design was used to quantify the effects of fuel arrangement on fire behavior with 3.66 m diameter treatments cut to a height of 0.15 m. The treatments ephemerally reduced fire rate of spread …

Investigating Risk Of Suboptimal Hiv Treatment Outcomes (Treatment Failure And Disengagement) Among Pregnant And Postpartum Women Living With Hiv, Kevin Owuor

All ETDs from UAB

The joint United Nations Programme on HIV/AIDS (UNAIDS) has set targets to end the HIV epidemic by improving HIV diagnosis, treatment, and viral suppression to reduce new infections and improve health outcomes for people living with HIV (PLHIV), including pregnant and postpartum women living with HIV (PPWH). After diagnosis, linking PPWH to antiretroviral (ART) treatment is critical to suppress the virus and prevent mother-to-child transmission (MTCT) of HIV. Continuous engagement in care is essential for achieving and maintaining virologic suppression in the peripartum and postpartum period for PPWH, both for their own health and the health of their family. Disengagement …

Predictive Modeling For Healthcare Data Using Nonlinear Bayesian Methods, Prince Kofi Asare

Theses and Dissertations

Unplanned hospital readmissions represent a significant challenge for healthcare systems, contributing to substantial financial burdens and highlighting gaps in patient care coordination. In the U.S., approximately 20% of Medicare beneficiaries are readmitted within 30 days, costing billions annually. Social determinants of health, such as income, housing stability, and social support, account for up to 80% of health outcomes, yet their integration into predictive models remains underexplored. This study introduces a novel Bayesian framework for predicting 30-day readmission risk, combining Gaussian Process models with spike-and-slab priors and Bayesian Lasso regression with Laplace priors. Utilizing Markov Chain Monte Carlo methods, the approach …

Check Your Data Before You Wreck Your Model: The Impact Of Careless Responding On Substance Use Data Quality, Abby L. Braitman, Anna M. Petrey, Jennifer L. Shipley, Rachel Ayala Guzman, Emily Renzoni, Alison Looby, Adrian J. Bravo

Psychology Faculty Publications

Background: The accuracy of survey responses is a concern in research data quality, especially in college student samples. However, examination of the impact of removing participants from analyses who respond inaccurately or carelessly is warranted given the potential for loss of information or sample diversity. This study aimed to understand if careless responding varies across a number of demographic indices, substance use behaviors, and the timing of survey completion.

Method: College students (N = 5809; 70.7% female; 75.7% White, non-Hispanic) enrolled in psychology classes from six universities completed an online survey assessing a variety of demographic and substance use-related information, …

Group Antenatal Care Positively Transforms The Care Experience: Results Of An Effectiveness Trial In Malawi, Crystal L. Patil, Kathleen F. Noor, Esnath Kapito, Li C. Liu, Xiaohan Mei, Elizabeth Chodzaza, Genesis Chorwe-Sungani, Ursula Kafuulafula, Elizabeth T. Abrams, Allissa Desloge, Ashley Gresh, Rohan D. Jeremiah, Dhruvi R. Patel, Anne Batchelder, Heidy Wang, Jocelyn Faydenko, Sharon S. Rising, Ellen Chirwa

Department of Medicine Faculty Publications

Background

We developed and tested a Centering-based group antenatal (ANC) model in Malawi, integrating health promotion for HIV prevention and mental health. We present effectiveness data and examine congruence with only the Group ANC theory of change model, which identifies key processes as supportive relationships, empowered partners in learning and care, and meaningful services, leading to better ANC experiences and outcomes.

Methods

We conducted a hybrid effectiveness-implementation trial at seven clinics in Blantyre District, Malawi, comparing outcomes for 1887 pregnant women randomly assigned to Group ANC or Individual ANC. Group effects on outcomes were summarized and evaluated using t-tests, Mann-Whitney, …

A New G Family: Properties, Characterizations, Different Estimation Methods And Port-Var Analysis For U.K. Insurance Claims And U.S. House Prices Data Sets, Ahmad M. Aboalkhair, Gholamhossein Hamedani, Nazar Ali Ahmed, Mohamed Ibrahim, Mohammad A. Zayed, Haitham M. Yousof

Mathematical and Statistical Science Faculty Research and Publications

This paper introduces a new class of probability distributions, termed the generated log exponentiated polynomial (GLEP) family, designed to enhance flexibility in modeling complex real financial data. The proposed family is constructed through a novel cumulative distribution function that combines logarithmic and exponentiated polynomial structures, allowing for rich distributional shapes and tail behaviors. We present comprehensive mathematical properties, including useful series expansions for the density, cumulative, and quantile functions, which facilitate the derivation of moments, generating functions, and order statistics. Characterization results based on the reverse hazard function and conditional expectations are established. The model parameters are estimated using various …

Early Entering Research And Writing (Eerw) In College-Level Statistics, Rebecca Fang

2025 Faculty Bibliography

With the high demand for data-driven knowledge, students today need to comprehend skills in problem-solving, critical thinking, communication, and collaboration. However, in traditional statistics lectures, students learn descriptive algorithms, hypothesis, and linear regression at their early stage of college. Unfortunately, they often analyze numbers without considering the context, purpose, audience, and the meaning of the numbers. Therefore, providing students the early opportunity to research and write with data in college will allow them to deepen their understanding of the subjects, to think critically about the data and the results, to communicate effectively with diverse audience, and to prepare for their …

Group And State-Specific Estimation In Animal Movement Models Using A Bayesian Approach, Anita Bhandari Sharma

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This research study investigates statistical approaches for modeling the movement patterns of white-tailed deer in Louisiana using GPS tracking data. We start by classifying the latent behavioral states using a hidden Markov model (HMM) and then integrate those inferred states into a state-dependent step selection framework to evaluate the land cover preferences. Standard HMMs, however, assume the same movement patterns for all animals, overlooking the differences due to characteristics such as sex, age, breeding season, etc.

To address this limitation, we extend the modeling framework to incorporate the group-level structure defined by similar characteristics or conditions to assess whether such …

Capital Structure Models And Contingent Convertible Securities, Di Meng

Theses and Dissertations (Comprehensive)

The 2007-09 financial crisis showed financial institutions are vulnerable during distressed times. As an alternative resolution to a government bail-out, contingent convertible securities (contingent capital or CoCos) were proposed by various researchers. CoCo is a hybrid capital security that converts from a bond to common equity when a pre-determined event occurs. The loss absorption mechanism of CoCo is essential to the financial health of a bank during a crisis as it provides an instant capital infusion when public capital is difficult to access.

In this thesis, we first implement a methodology to calibrate capital structure models for large Canadian banks. …

Using Landscape Ecology And Spatial Statistics To Examine The Impacts Of Proposed Removals To Natural Heritage System And The Agricultural System Of Ontario’S Greenbelt, Brianna Downey

Theses and Dissertations (Comprehensive)

The 2022 proposed removals from the Greater Toronto Area (GTA), Southern Ontario’s Greenbelt would have resulted in negative impacts including, reductions to the size and functionality of the Agricultural System and Natural Heritage System, which are components of protected Greenbelt area. Several removal sites were located either on or in close proximity to corridor areas of the NHS, reducing connectivity and negatively impacting the surrounding ecological area. The removal of Agricultural land primarily consisted of corn and soybeans, as well as large removals of woodland, wetland, and shrubland class areas. The removal sites on local Agricultural composition and configuration were …

Analysis Of Cytokine Data In A Case-Control Study Of Me/Cfs, Navya Amaratunga

Electronic Theses & Dissertations (2024 - present)

This study investigated the role of cytokines in Myalgic Encephalomyelitis/Chronic Fatigue Syndrome (ME/CFS), a debilitating multi-system disease with unknown etiology. Using data from a case-control study (60 cases, 61 controls) previously collected by Dr. Roxana Moslehi’s lab, serum levels of 48 cytokines were analyzed. Statistical analyses, including T-tests, Wilcoxon Rank Sum tests, and logistic regression (unadjusted and adjusted for medication use), were performed to identify differences between cases and controls.

Results revealed a statistically significant difference in mean Fractalkine levels between cases and controls (p=0.031). Borderline significant differences were also observed for IL-6 (p=0.046) and MIP-1α (p=0.046). Unadjusted logistic regression …

Complex Missing Data Problems In Education Surveys, Thomas Wesley Robertson

Electronic Theses & Dissertations (2024 - present)

Missing data are a nearly universal problem in human subjects research, including in education. However, reporting and addressing missing data is an issue, despite guidelines from the APA style guide and the What Works Clearinghouse, as well as guidance from prominent statisticians on the best methods to use. Prior research conducted in 2004 and 2014 found that in the field of education, most studies do not report or address missing data. In addition, no study has looked specifically at how missing data are reported and addressed in complex surveys. The current study has two main objectives: first, to determine if …

Safeguard Cyberspace In Ransomware Era: Risk Analysis & Cyber Insurance, Li Huang

Electronic Theses & Dissertations (2024 - present)

The increasing frequency and severity of ransomware attacks pose significant challenges for organizational cybersecurity. Fragmentation across disciplines in cyber defense has created practical gaps in the development of the necessary capabilities needed to address rapidly evolving cyber threats. This study explores the impact of ransomware attacks and the evolving role of cyber insurance as a proactive cybersecurity partner. Bridging the gap between actuarial science and cyber risk management, it proposes an interdisciplinary framework that quantifies the impact of ransomware and integrates cyber insurance into cybersecurity strategies.

The primary contribution of this study is methodology. We present a framework that remains …

A Two-Stage Design For Choosing Among Several Normal Treatments In Comparison With A Control: The Case Of Common, Known Variance, Samarasuriyage Sayura Sankalpa Senaratne

UNF Graduate Theses and Dissertations

A two-stage design is developed for comparing the means of multiple normally distributed treatment groups under a known common variance, with the aim of identifying the treatment with the highest mean while minimizing the expected sample size, a crucial consideration in clinical trials. The proposed methodology integrates elements of both hypothesis testing and selection procedures to achieve greater efficiency and decision-making power. In the initial stage, if no treatment exhibits a mean surpassing a predefined efficacy threshold, the trial is terminated early, conserving resources. If one or more treatments exceed the threshold, the procedure advances to a second stage, where …