Statistics and Probability Commons^™

Stochastic Optimal Control Of Conditional Mckean-Vlasov Equations With Jump And Markovian Switching, Charles Samuel Conly Sharp

Theses and Dissertations

This thesis obtains a number of results in stochastic optimal control for conditional McKean-Vlasov equations with jump and Markovian switching. First, we prove the uniqueness of the solutions and derive a relevant version of Itô's formula. We provide the dynamic programming principle and prove the associated verification theorem. A stochastic maximum principle is established. Further, we derive the relationship between dynamic programming and the stochastic maximum principle. Additionally, we utilize our stochastic maximum principle result for a mean-variance portfolio selection problem.

The Private Pilot Check Ride: Applying The Spacing Effect Theory To Predict Time To Proficiency For The Practical Test, Michael Scott Harwin

Theses and Dissertations

This study examined the relationship between a set of targeted factors and the total flight time students needed to become ready to take the private pilot check ride. The study was grounded in Ebbinghaus’s (1885/1913/2013) forgetting curve theory and spacing effect, and Ausubel’s (1963) theory of meaningful learning. The research factors included (a) training time to proficiency, which represented the number of training days needed to become check-ride ready; (b) flight training program (Part 61 vs. Part 141); (c) organization offering the training program (2- or 4-year college/university vs. FBO); (d) scheduling policy (mandated vs. student-driven); and demographical variables, which …

Steady State Thermal Blooming With Convection: Modeling, Simulation And Analysis, Jeremiah S. Lane

Theses and Dissertations

The modeling, simulation, and analysis of high energy laser propagation is a research topic of significant interest to the defense community. A detailed understanding of the phenomenon of thermal blooming is crucial as it is detrimental to the propagation of lasers over long distances and in the presence of aerosols. The simulation of thermal blooming has historically relied on wave optics models and scaling laws for the fluid response to the laser. Since thermal blooming occurs in the presence of natural convection, however, there is a need for simulating this coupled fluid-beam effect using a first principles approach. In this …

Improving Deep Reinforcement Learning Methodology For Autonomous Defense And Escort Of Military High-Value Assets, Joseph Liles Iv

Theses and Dissertations

This dissertation explores the application of machine learning to the control of autonomous unmanned combat aerial vehicles (AUCAVs). In particular, this research applies deep reinforcement learning methodologies to a defensive air combat scenario wherein a fleet of AUCAVs protects a military high-value asset (HVA). A collection of air battle management scenarios along with an original simulation environment and a set of designed computational experiments support the approximation of high-quality decision policies by employing Markov decision processes, approximate dynamic programming algorithms, and deep neural networks for value function approximation.

Advanced Statistical Methodology For The Modern Probability Of Detection, Christine E. Knott

Theses and Dissertations

Probability of detection (POD) is an invaluable part of the calculations used by the USAF to validate the capabilities of nondestructive inspection systems for detecting defects in critical structural components on aircraft. A POD study consists of a designed experiment, linear modeling, and a probability of detection verses defect size curve. This curve is useful for determining how often an aircraft should be re-inspected. Some POD studies are unsuccessful in creating realistic POD curves because the statistical modeling used has two common limitations: (1) a lack of convergence leading to no solution and, (2) violated assumptions leading to incorrect solutions. …

Approaches To Detecting And Modeling Over-And Underdispersion In Alternative Count Data Distributions And An Application Of Logistic Regression And Random Forest Modeling To Improve Screening Tools For Tic Disorders In Children, Rebecca C. Wardrop

Theses and Dissertations

This dissertation focuses on theory and application of discrete data methods, particularly approaches to over- and underdispersion relative to the Poisson distribution and an application of random forest and logistic regression modeling. The first chapter derives a score test for over- and underdispersion in the heaped generalized Poisson distribution. Equi-, over-, and underdispersed heaped generalized Poisson and heaped negative binomial data are simulated to evaluate the performance of the score test by comparing the power it achieves to that of Wald and likelihood ratio tests. We find that the score test we derive performs comparably to both the Wald and …

Statistical Methods For Single Cell Sequencing Data Analysis, Fei Qin

Theses and Dissertations

The recent emergence of single cell sequencing (SCS) technology has provided us with single-cell DNA or RNA sequencing (scDNA/RNA-seq) information to investigate cellular evolutionary relationships. Despite many analysis methods have been developed to infer intra-tumor genetic heterogeneity, cluster cellular subclones, detect genetic mutations, and investigate spatially variable (SV) genes, exploring SCS data remains statistically challenging due to its noisy nature.

To identify subclones with scDNA-seq data, many existing studies use an independent statistical model to detect copy number profile in the first step, followed by classical clustering methods for subclone identification in downstream analyses. However, spurious results might be generated …

A Bayesian Spatial Scan Statistic For Normal Data, Laasya Velamakanni

Theses and Dissertations

Scan statistics are useful methods for detecting spatial clustering. While they were initially developed to detect regions with an excess of binomial or Poisson events, spatial scan statistics have been extended to detect hotspots in other types of data including continuous data. They have many applications in different fields such as epidemiology (e.g. detecting disease outbreaks), sociology (e.g. detecting crime hotspots), and environmental health (e.g. detecting high-pollution areas). Spatial scan statistics identify a ‘most likely cluster’ and then use a likelihood ratio test to determine if this cluster is statistically significant. Spatial scan statistics have been extended to the Bayesian …

Detecting Gene-Gene Or Gene Environment Interactions In Association With Complex Disease Outcomes, Taiwo Adetunji Famuyiwa

Theses and Dissertations

Identifying gene–gene and gene–environment interaction is complicated and gainsaying most especially because of high multifactor dimensions involve in the analysis of such combination discrediting the functionality of parametric statistical method like Logistic Regression. [22] developed a multi-factor-dimensionality reduction (MDR) method for detecting and characterizing high-order gene-gene and gene-environment interactions in case-control and discordant-sib-pair studies with relatively small samples, which is inspired by the combinatorial partitioning method of [18]. [16] proposed Generalized MDR (GMDR) framework based on the score of a generalized linear model which allows adjustment of covariates, provides a unified framework for handling both dichotomous and quantitative phenotypes. However, …

Identifying Limitations In Using Diagnostic Testing For Absorption Of Passive Maternal Immunity In Neonatal Beef Calves To Predict Pre-Weaning Disease, Alexis Charlotte Thompson

Theses and Dissertations

Calves are born agammaglobulinemic and rely on colostrum consumption for the transfer of maternal passive immunity. Calves that fail to absorb adequate amounts of maternal antibodies from colostrum are commonly referred to as having failed transfer of passive immunity (FTPI). The overall aim of this dissertation was to explore the usefulness of FTPI testing in neonatal beef calves to predict their risk for subsequent illness or death. The objectives were to evaluate the impact of FTPI on pre-weaning disease in beef and dairy calves, quantify and compare the variance in IgG concentrations measured by radial immunodiffusion and serum total protein …

A Machine Learning Approach To Obese-Inflammatory Phenotyping, Tania Mayleth Vargas

Theses and Dissertations

Obesity is the accumulation of an abnormal, or excessive, amount of fat in the body, which can have negative effects on overall health. This excess accumulation of macronutrients in adipose tissue can cause the release of inflammatory mediators, leading to a proinflammatory state. Inflammation is a known risk factor for various health conditions, including cardiovascular diseases, metabolic syndrome, and diabetes. This study sought to examine the use of data mining methods, particularly clustering algorithms, to identify inflammatory biomarker phenotypes and their association with obesity in a local adolescent population. The algorithms evaluated in this study included: k-means, Ward's hierarchical …

A Machine Learning Approach To Evaluate The Effect Of Sodium-Glucose Cotransporter-2 Inhibitors On Chronic Kidney Disease In Diabetes Patients, Solomon Eshun

Theses and Dissertations

Chronic kidney disease (CKD) is a significant complication that contributes to diabetes-related mortality in the United States, and there is growing evidence that sodium-glucose cotransporter 2 inhibitors (SGLT2i) can slow its progression. However, observational studies may suffer from confounding by indication, where patient characteristics and disease severity influence the decision to prescribe SGLT2i. This study utilized electronic health records of individuals with diabetes (from TriNetX) to investigate the effectiveness of SGLT2i on CKD progression. The database provided detailed information on patients’ CKD status, demographics, diagnosis, procedures, and medications, along with corresponding dates of diagnosis and prescription. The study comprised of …

Bayesian Dependence Structure Analysis For Ordinal Data, Yang He

Theses and Dissertations

This dissertation explores different methods to study the dependence structure among many ordinal variables under the Bayesian framework.

Chapter 1 introduces ordinal data analysis methods, and the related literature works are briefly reviewed. An outline of the dissertation is put forward.

In Chapter 2, Gaussian copula graphical models with different priors of graphical Lasso, adaptive graphical Lasso, and spike-and-slab Lasso on the precision matrix are assessed and compared. The proposed models are well illustrated via simulations and a real ordinal survey data analysis.

In Chapter 3, adaptive spike-and-slab Lasso prior is proposed as an extension of Chapter 2. The developed …

Survival Models With Background Mortality, Shujie Chen

Theses and Dissertations

In this dissertation, we focus on studying three mixture cure models with background mortality. With the development of treatment, patients may be cured and suffer from other cause of death. The cure model with background mortality can measure the population cure which refers to the patients with comparable mortality with their counterpart in general population. Three types of survival models are investigated, including generalized odds rate (GOR) model, cure model with background mortality for right censoring and interval censoring, and extended illness death model via incorporating “cure” fraction. All methods are validated via comprehensive simulation studies and real data application. …

Advancements In Parametric Modal Regression, Qingyang Liu

Theses and Dissertations

This dissertation considers statistical inference methods for parametric modal regression models. In Chapter 1, we motivate the mode as the measure of central tendency instead of the median or the mean with an example. Following the motivational example, we include an overview of existing modal regression models. Later, in the same chapter, we explain advantages of the parametric modal regression models over existing nonparametric modal regression models. In Chapter 2, we address issues in statistical inference brought in by data contaminated with measurement error. With measurement error in covariates, statistical inference methods designed for modal regression models with error-free covariates …

Detecting Spatially Varying Coefficient Effects With Conditional Autoregressive Models: A Simulation Study Using Social Determinants Of Health Screening Data, Reid J. Demass

Theses and Dissertations

Generalized linear models which include spatially varying coefficient terms allow researchers to determine if the association between predictor and outcome variables vary across geographic space. Such models are particularly applicable to research with public health data where interventions and limited health care resources must be allocated carefully. The integrated nested Laplace approximation (INLA) methodology available in the R INLA package is a popular tool to estimate spatially varying coefficients. To assess the performance of the estimation procedure, patient emergency department (ED) visits were simulated from data sourced from a pilot study at Prisma Health. The INLA technique was used to …

Sparse Partitioned Empirical Bayes Ecm Algorithms For High-Dimensional Linear Mixed Effects And Heteroscedastic Regression, Anja Zgodic

Theses and Dissertations

Variable selection methods in both the frequentist and Bayesian frameworks are powerful techniques that provide prediction and inference in high-dimensional linear regression models. These methods often assume independence between observations and normally distributed errors with the same variance. In practice, these two assumptions are often violated. To mitigate this, we develop efficient and powerful Bayesian approaches for linear mixed modeling and heteroscedastic linear regression. These method offers increased flexibility through the development of empirical Bayes estimators for hyperparameters, with computationally efficient estimation through the Expectation Conditional-Minimization (ECM) algorithm. The novelty of these approaches lies in the partitioning and parameter expansion, …

Examining Fuel Service System Failures Of The Usaf R11 Using Survival Analysis, Roed M.S. Mejia

Theses and Dissertations

Recent events show that fuel supply is a large contributor to the success or failure of a military operation in response to a contingency. Any future near-peer conflict will stress the supply chain and require fully operational vehicles to be ready for the primary mission sets they support. In the United States Air Force (USAF), the readiness of fuel distribution trucks is crucial to meeting those mission sets in global operations. Utilizing non-parametric and semi-parametric survival models, which do not assume specific probability distributions, this study analyzes maintenance data for R-11 trucks that refuel aircraft.

Examining Failures Of Kc-135 Boom Assemblies Using Survival Analysis, Benjamin D. Miller

Theses and Dissertations

The purposes of this study are to confirm the applicability of survival analysis for predicting recurrent failures of a component of a military aircraft and to provide practical insights to maintenance managers and mission planners. The results of this study also can help the United States Department of Defense improve the CBM+ program. This study was able to predict recurrent failures of the component using Nelson-Aalen cumulative estimates. In addition, this study used a Cox proportional hazards regression model with shared frailty for measuring the effect of covariates on recurrent failures and unidentified heterogeneity in the model, which warranted future …

Probability Of Agreement As A Simulation Validation Methodology, Matthew C. Ledwith

Theses and Dissertations

Determining whether a simulation model is operationally valid requires the rigorous assessment of agreement between observed functional responses of the simulation model and the corresponding real world system or process of interest. This research seeks to extend and formulate the probability of agreement approach to the operational validation of simulation models. The first paper provides a methodological approach and an initial demonstration which leverages bootstrapping to overcome situations where one’s ability to collect real-world data is limited. The second paper extends the probability of agreement approach to account for second-order heteroscedastic variability structures and establishes a weighted probability of agreement …

Debris Survivability Study For Mega-Constellation Architectures, Joseph C. Canoy

Theses and Dissertations

The analysis for the overall theoretical debris survivabilty of mega-constellation architectures, with an emphasis on space-based ballistic missile defense constellation (SB-BMD), is explored via three extensive different Monte Carlo simulations: preliminary analysis of low Earth Orbit (LEO) mega-constellation survivabilty following a fragmentation event within the constellation, analysis of LEO mega-constellation survivability with a fragmentation event occurring on a satellite performing a maneuver to insert itself within the constellation, and the analysis of LEO mega-constellation survivabilty after a fragmentation event resulting from the destruction of a missile. The LEO mega-constellations represent the SB-BMD constellation. The first two analysis sections will include …

Variability In Causal Effects On A Binary Outcome And Noncompliance In A Multisite Randomized Trial, Xinxin Sun

Theses and Dissertations

Noncompliance to treatment assignment is widespread in randomized trials and presents challenges in causal inference. In the presence of noncompliance, the most commonly estimated effect of treatment assignment, also known as intent-to-treat (ITT) effect, is biased. Of interest in this setting is the complier average causal effect (CACE), the ITT effect among compliers. Further complication arises when the outcome variable is partially observed.

My research focuses on estimating the distribution of a site-specific CACE in a multisite randomized controlled trial (MRCT) by maximum likelihood (ML). Assuming compliance missing at random (MAR). We express the likelihood as an integral with respect …

Reassessing Replication: Addressing The Replication Crisis From A Statistical Perspective, Alicia Richards Phd

Theses and Dissertations

In 2015, Open Science Framework directly replicated 100 psychology studies and found astonishingly low replication rates. Since, researchers have suggested factors that may have influenced the low rates, including the metrics used to assess replications. The definitions used to decide whether a replication study was successful all suffer from flaws. Therefore, we propose a new metric for assessing replication that can estimate the likelihood a study successfully replicated rather than forcing a binary choice and accounts for study design limitations.

Using equivalence study techniques, we first propose a new metric to assess replication, defining a successful replication as one where …

Early Termination In Phase Ii Clinical Trials: Admissible Designs Using Decreasingly Informative Priors, Chen Wang

Theses and Dissertations

In Phase II clinical trials, Thall and Simon’s Bayesian posterior probability design is commonly implemented to allow for an early termination to determine whether a new treatment warrants further investigation in a larger-scale Phase III trial; this in turn requires a pre-selected prior distribution based on known clinical opinion or historical information. Moreover, this Bayesian approach can result in an issue of inflating type I error rate by monitoring interim data to inform early termination decisions. Alternatively, a Bayesian approach with the decreasingly informative prior (DIP), which is an informative yet skeptical prior, can be implemented to overcome the contentious …

Model-Based Imputation Of Below Detection Limit Missing Data And Group Selection In Bayesian Group Index Regression, Matthew Carli

Theses and Dissertations

Investigations into the association between chemical exposure and health outcomes are increasingly focused on the role of chemical mixtures, as opposed to individual chemicals. The analysis of chemical mixture data required the development of novel statistical methods, one of these being Bayesian group index regression. A statistical challenge common to all chemical mixture analyses is the ubiquitous presence of below detection limit (BDL) data. We propose an extension of Bayesian group index regression that treats both regression effects and missing BDL observations as parameters in a model estimated through a Markov Chain Monte Carlo algorithm that we refer to as …

Integrative Post-Gwas Analyses Of Psychiatric Disorders: Identifying Putative Risk Genes And Gene Sets Using Transcriptome, Proteome And Methylome Information, Huseyin Gedik

Theses and Dissertations

Genome-wide association studies (GWAS) of psychiatric disorders (PD) yield numerous loci with significant signals, but often they do not implicate specific protein coding genes. Because GWAS risk loci are enriched in expression/protein/methylation quantitative loci (e/p/mQTL, hereafter xQTL), transcriptome/proteome/methylome-wide association studies (T/P/MWAS, hereafter XWAS), which integrate information from GWAS and x-level (mRNA, protein or DNA methylation levels) coming from largest xQTL studies, can link GWAS signals to effects on specific genes. For gene level analyses, researchers use mendelian randomization (MR) methods to fine-map the association between x-levels and trait. However, none of the previous studies ever jointly analyzed XWAS of multiple …

Dynamics Of Redox-Driven Molecular Processes In Local And Systemic Plant Immunity, Philip Berg

Theses and Dissertations

The work here presents two main parts. In the first part, chapters 1 – 3 focus on dynamical systems modeling in plant immunity, whereas chapters 4 – 6 describe contributions to computational modeling and analysis of proteomics and genomics data. Chapter 1 investigates dynamical and biochemical patterns of reversibly oxidized cysteines (RevOxCys) during effector-triggered immunity (ETI) in Arabidopsis, examines the regulatory patterns associated with Arabidopsis thimet oligopeptidase 1 and 2’s (TOP1 and TOP2), roles in the RevOxCys events during ETI, and analyzes the redox phenotype of the top1top2 mutant. The second chapter investigates the peptidome dynamics during ETI …

Towards Structured Planning And Learning At The State Fisheries Agency Scale, Caleb A. Aldridge

Theses and Dissertations

Inland recreational fisheries has grown philosophically and scientifically to consider economic and sociopolitical aspects (non-biological) in addition to the biological. However, integrating biological and non-biological aspects of inland fisheries has been challenging. Thus, an opportunity exists to develop approaches and tools which operationalize planning and decision-making processes which include biological and non-biological aspects of a fishery. This dissertation expands the idea that a core set of goals and objectives is shared among and within inland fisheries agencies; that many routine operations of inland fisheries managers can be regimented or standardized; and the novel concept that current information and operations can …

Weather Parameters Influencing The Incidence Of Citrus Canker Caused By Aw Strain In The Rio Grande Valley, Amit Sharma

Theses and Dissertations

Citrus canker caused by bacterium Xanthomonas citri subsp. citri (Xcc) seriously affects the citrus industry by making the fruit unmarketable due to unsightly lesions on the fruit. Canker caused by Aw strain of Xcc was reported in the citrus trees located in the residential areas of the Rio Grande Valley (RGV). Canker severity differs amongst cultivars/varieties, and it is influenced by prevailing environmental conditions. Multiple regression modeling of the disease incidence with the environmental variables such as temperature, humidity, windspeed, wind gust, and rainfall was performed to understand the environmental conditions that are favorable for spread of citrus …

Topics In Multilevel Mediation Analysis, Chung Li Wu

Theses and Dissertations

A proper study design assures adequate power to detect statistically significant differences. Existing power calculations for multilevel mediation analysis make a strong distributional assumption of normality. However, binary outcomes are commonly seen in real-world study. Motivated by this fact, we conduct a simulation-based power study for a multilevel mediation analysis with binary outcomes. The numbers of participants needed to achieve 80% power are summarized in tables for future reference.

Mixed-effect regression is commonly used in multilevel analysis for panel data. Yet, the estimated coefficients from the random-intercept model could represent either purely between-cluster, purely within-cluster, or weighted-average effects. Therefore, we …