Statistics and Probability Commons^™

Incorporating Effects-Based Approaches Into Environmental Impact Assessment To Improve Post-Development Monitoring, Carolyn J M Brown

Theses and Dissertations (Comprehensive)

Over the last 50 years, improvements in design of industrial facilities have significantly reduced environmental impacts. But impacts still occur and monitoring programs are the main mechanism to inform when modification/implementation of mitigation is needed. Informed decisions require adequate baseline (pre-development) data to predict impacts based on the development’s design and to understand when the post-development environment has changed. An adaptive monitoring plan provides an effective way to evaluate monitoring results and allow for proactive responses to environmental change before impacts become difficult or challenging to reverse. Unfortunately, baseline data gathered during an environmental impact assessment (EIA) is often inadequate …

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Last Passage Time And Excursion Theory For Solvable Diffusions With Applications In Mathematical Finance, Yaode Sui

Theses and Dissertations (Comprehensive)

In this dissertation, we investigate the properties of last passage times and excursion theory in one-dimensional solvable diffusions, emphasizing their applications in financial modeling, particularly in option pricing. We derive closed-form formulas for the marginal distribution of last passage times and their joint distribution with process values, including the maximum and minimum of the process value. The focus is on time-homogeneous diffusions with various boundaries and imposed killing. Employing spectral expansion theory, we derive explicit formulas for distributions of last passage times in common processes such as Drifted Brownian Motion (BM), Squared Bessel (SQB), Ornstein-Uhlenbeck (OU), and Cox-Ingersoll-Ross (CIR) models. …

Examining Information Systems Use To Facilitate The Workplace Accommodation Process, Shiya Cao

Statistical and Data Sciences: Faculty Publications

BACKGROUND: The workplace accommodation process is often affected by ineffective and inefficient communications and information exchanges among disabled employees and other stakeholders. Information systems (IS) can play a key role in facilitating a more effective and efficient accommodation process since IS has been shown to facilitate business processes and effect positive organizational changes.

OBJECTIVE: Since there is little to no research that exists on IS use to facilitate the workplace accommodation process, this paper, as a critical first step, examines how IS have been used in the accommodation process.

METHODS: Thirty-six interviews were conducted with disabled employees from various organizations. …

Questions (And Answers) For Incorporating Nontraditional Grading In Your Statistics Courses, Brenna Curley

Statistical and Data Sciences: Faculty Publications

Nontraditional grading methods have recently become more common, and as with any large pedagogical shift, there are a number of questions to consider when applying a new grading scheme to a course. This article summarizes four types of nontraditional grading and shares experiences from the authors who have applied them to a variety of courses in statistics. This article is structured as a set of questions and answers, seeking to address many of the concerns and considerations that one may face as they transition a course’s grading structure. Supplementary materials for this article are available online.

Correction: Bayesian Kinetic Modeling For Tracer-Based Metabolomic Data, Xu Zhang, Ya Su, Andrew N. Lane, Arnold Stromberg, Teresa Whei-Mei Fan, Chi Wang

Statistics Faculty Publications

No abstract provided.

Bayesian Variable Selection With Shrinkage Priors And Generative Adversarial Networks For Fraud Detection, Amina Issoufou Anaroua

Graduate Thesis and Dissertation 2023-2024

This research paper focuses on fraud detection in the financial industry using Generative Adversarial Networks (GANs) in conjunction with Uni and Multi Variate Bayesian Model with Shrinkage Priors (BMSP). The problem addressed is the need for accurate and advanced fraud detection techniques due to the increasing sophistication of fraudulent activities. The methodology involves the implementation of GANs and the application of BMSP for variable selection to generate synthetic fraud samples for fraud detection using the augmented dataset. Experimental results demonstrate the effectiveness of the BMSP GAN approach in detecting fraud with improved performance compared to other methods. The conclusions drawn …

Deep Learning One-Class Classification With Support Vector Methods, Hayden D. Hampton

Graduate Thesis and Dissertation 2023-2024

Through the specialized lens of one-class classification, anomalies–irregular observations that uncharacteristically diverge from normative data patterns–are comprehensively studied. This dissertation focuses on advancing boundary-based methods in one-class classification, a critical approach to anomaly detection. These methodologies delineate optimal decision boundaries, thereby facilitating a distinct separation between normal and anomalous observations. Encompassing traditional approaches such as One-Class Support Vector Machine and Support Vector Data Description, recent adaptations in deep learning offer a rich ground for innovation in anomaly detection. This dissertation proposes three novel deep learning methods for one-class classification, aiming to enhance the efficacy and accuracy of anomaly detection in …

Numerical Investigation And Statistical Analysis Of The Flow Patterns Behind Square Cylinders Arranged In A Staggered Configuration Utilizing The Lattice Boltzmann Method, M. Abid, N. Yasin, M. Saqlain, S. Ul-Islam, S. Ahmad

Mathematics & Statistics Faculty Publications

Flow past bluff bodies like square cylinders is important in engineering applications, but flow patterns behind staggered cylinder arrangements remain poorly understood. Existing studies have focused on tandem or side-by-side configurations, while offset orientations have received less attention. The aim of this paper is to numerically investigate flow dynamics and force characteristics behind two offset square cylinders using the single relaxation time lattice Boltzmann method. The effects of changing both the Reynolds number (Re = 1-150) and gap spacing ratio (g* = 0.5-5) between the cylinders are analyzed. Instantaneous vorticity contours, time histories of drag and lift coefficients, power spectra …

Integrating Machine Learning With Cure Models And Associated Inference, Wisdom Aselisewine

Mathematics Dissertations - Archive

Recent advancements in medical treatments have significantly enhanced the rates of recovery for numerous chronic illnesses. This progress has sparked growing interest in developing suitable statistical models capable of handling survival data that includes substantial cure fractions. The mixture cure model finds extensive application in analyzing survival data when there exists a cured subgroup. Standard logistic regression-based approaches for modeling the incidence part of the mixture cure model may suffer from poor predictive accuracy, especially in the presence of high dimensional covariates and/or non-linear covariate effects. To overcome this limitation, we propose the integration of distinct machine learning algorithms with …

The Performance Of Marginal Modeling Methods For Rare Events With Application To Opioid Overdose Mortality And Morbidity, Shawn Nigam

Theses and Dissertations--Epidemiology and Biostatistics

Opioid misuse is a nationwide epidemic, with Kentucky having one of the highest opioid overdose-related fatality rates across all US states. These rates have increased significantly over the past decade, with particularly large increases during the COVID-19 pandemic. This dissertation aims to study the behavior of these increases and the methods for the marginal modeling of count outcomes related to opioid overdose.

Opioid overdose-related fatality rates in Kentucky increased significantly during the COVID-19 pandemic. In this chapter, we characterize the changes in opioid overdose fatality rates in Kentucky and identify associations between potential factors and fatality rates. County-level opioid overdose …

Variable Selection For High-Dimensional Data With Interaction Effects: Methods, Applications, And Inferences, Leiyue Li

Theses and Dissertations--Statistics

For high-dimensional data where the number of variables greatly exceeds the number of observations, selecting important variables while maintaining the required heredity conditions can be challenging. This dissertation is structured into three interconnected parts. In the first part, we propose a variable selection method by implementing a well-known optimization technique, the Genetic Algorithm. An R package was developed to simplify the implementation and usage of the proposed method. We then propose another variable selection method by extending the study from the Genetic Algorithm to a different but related optimization technique, Simulated Annealing. We consider three different hierarchical structures in both …

High-Dimensional Tests And Projection Methods: Subvector Analysis And Matrix Variate Data, Shouryya Mitra

Theses and Dissertations--Statistics

In this dissertation, we study projection-based methods to testing problems for high-dimensional data. We also investigate inferential methods for matrix variate data with block compound symmetry (BCS) covariance structure. The research reported in dissertation consists of three projects.

The first project addresses power loss and ill-conditioned error covariance estimates commonly faced by multivariate tests in high-dimensional settings. To overcome these challenges, previous approaches avoided correlations in constructing test statistics, but this required strong assumptions about covariance matrices and dependence structures. More recently, some methods have incorporated correlations by employing random projection into a lower-dimensional space. We develop a unified framework …

Estimation And Testing Of Nonparametric Effects Of Incomplete Multivariate And Repeated Measures Data, Swetalina Maity

Theses and Dissertations--Statistics

In this dissertation, we investigate three distinct but interrelated problems in analyzing repeated measure data with missing values.

The first project is on semiparametric methods for analyzing repeated measures designs with missing values. A closed-form estimator for the parameters and their asymptotic covariance are derived using block partitioning based on the missing data pattern. We also derive the asymptotic distribution of the estimators and construct test statistics to test hypothesis formulated as linear contrasts of the mean vector.

In the second project, we focus on purely nonparametric methods. In this setup, nonparametric treatment effects are defined as functionals of the …

From Non-Parametric Methods To Self-Supervised Learning: Applications In Edge Detection And Image Denoising, Jiacheng Xu

Theses and Dissertations--Statistics

This dissertation explores advanced methodologies for edge detection and image denoising through the application of both traditional non-parametric methods and modern self-supervised deep learning techniques. Beginning with non-parametric approaches, we refine surface fitting and jump detection criteria to enhance the detection of discontinuous regression surfaces in grayscale images. These foundational techniques are extended to color images, with analyses across RGB and CIELAB color spaces to improve edge detection accuracy. We then introduce a self-supervised neural network model that integrates Masked Modeling into the Bi-Directional Cascade Network (BDCN) framework. This approach shows the potential of reducing the dependency on annotated data …

Patterns Into Pathways For Improving Safety Culture: Refined Latent Class Analysis Informs Tailored Decision Support For South Carolina Dss Safety Culture Improvements, Michaela Voit

Theses and Dissertations--Public Health (M.P.H. & Dr.P.H.)

The rising prevalence of exposures to adverse childhood experiences (ACEs) demands a coordinated public health response, as a significant body of research details the cumulative impact of ACEs on chronic morbidities contributing to reduced life expectancy. Child welfare workers (CWW) are embedded in this public health effort, tasked with preventing and mitigating the impacts of ACEs through family and prevention services. The National Partnership for Child Safety (NPCS) may improve the wellbeing of CWWs and the effectiveness of Child Welfare (CW) services by improving the quality of safety culture within CW organizations. To inform NPCS quality improvement efforts, our project …

Stigma And Efficacy Beliefs Regarding Opioid Use Disorder Treatment And Naloxone In Communities Participating In The Healing Communities Study Intervention, Nicky Lewis, Barry Eggleston, Redonna K. Chandler, Dawn Goddard-Eckrich, Jamie E. Luster, Dacia Beard, Emma Rodgers, Rouba A. Chahine, Philip M. Westgate, Shoshana N. Benjamin, Janae Holloway, Thomas Clarke, R. Craig Lefebvre, Michael D. Stein, Donald W. Helme, Jennifer Reynolds, Sharon L. Walsh, Darcy Freedman, Nabila El-Bassel, Kara Stephens, Anita Silwal, Michelle R. Lofwall, Janet E. Childerhose, Hilary L. Surratt, Brooke N. Crockett, Amy L. Farmer, James L. David, Laura Fanucchi, Judy Harness, Ben Wilburn, Kelli Bursey, Kristin Mattson, Sarah Mann, Rebecca D. Jackson, Aimee Shadwick, Katherine Calver, Deborah Chassler, Jennifer Kimball, Nancy Regan, Jeffrey H. Samet, Rachel Sword-Cruz, Michael D. Slater

Biostatistics Faculty Publications

Background The HEALing Communities Study (HCS) included health campaigns as part of a community-engaged intervention to reduce opioid-related overdose deaths in 67 highly impacted communities across Kentucky, Massachusetts, New York, and Ohio. Five campaigns were developed with community input to provide information on opioid use disorder (OUD) and overdose prevention, reduce stigma, and build demand for evidence-based practices (EBPs). An evaluation examined the recognition of campaign messages about naloxone and whether stigma and efficacy beliefs regarding OUD treatment and naloxone changed in HCS intervention communities.

Methods Data were collected through surveys offered on Facebook/Instagram to members of communities participating in …

Pitching The Use Of Squared And Interaction Terms In Regression Via Baseball Heat Maps, Lucas Chepelsky

Williams Honors College, Honors Research Projects

This project will examine the impact of using second-order terms in regression. For illustration, we use an example of regression where a baseball player's three by three heat map, including the height and distance from inside to outside of the pitch, are variables used to predict batting average. We find that second-order terms are crucial in discovering nonlinear relationships and interaction effects in regression models, and maintain that the common practice of using first-order additive models is insufficient.

Multiple Imputation For Robust Cluster Analysis To Address Missingness In Medical Data, Arnold Harder, Gayla R. Olbricht, Godwin Ekuma, Daniel B. Hier, Tayo Obafemi-Ajayi

Mathematics and Statistics Faculty Research & Creative Works

Cluster Analysis Has Been Applied To A Wide Range Of Problems As An Exploratory Tool To Enhance Knowledge Discovery. Clustering Aids Disease Subtyping, I.e. Identifying Homogeneous Patient Subgroups, In Medical Data. Missing Data Is A Common Problem In Medical Research And Could Bias Clustering Results If Not Properly Handled. Yet, Multiple Imputation Has Been Under-Utilized To Address Missingness, When Clustering Medical Data. Its Limited Integration In Clustering Of Medical Data, Despite The Known Advantages And Benefits Of Multiple Imputation, Could Be Attributed To Many Factors. This Includes Methodological Complexity, Difficulties In Pooling Results To Obtain A Consensus Clustering, Uncertainty Regarding …

A Case Study On Variations In Network Structure And Cross- Sector Alignment In Two Local Systems Serving Pregnant And Parenting Women In Recovery, Liza M. Creel, Yana Feygin, Madeline Shipley, Deborah Winders Davis, Tiffany Cole Hall, Chaly Downs, Stephanie Hoskins, Natalie Pasquenza, Scott D. Duncan

Biostatistics Faculty Publications

Objective: To describe network structure and alignment across organizations in healthcare, public health, and social services sectors that serve pregnant and parenting women with substance use disorder (SUD) in an urban and a rural community.

Data Sources and Study Settings: Two community networks, one urban and one rural with each including a residential substance use treatment program, in Kentucky during 2021.

Study Design: Social network analysis measured system collaboration and cross-sector alignment between healthcare, public health, and social services organizations, applying the Framework for Aligning Sectors. To understand the alignment and structure of each network, we measured network density overall …