Statistics and Probability Commons^™

Factors Influencing Intent To Take A Covid-19 Test In The United States, Sheila Rutto

Theses and Dissertations

In 2020, COVID-19 became the first pandemic in the world’s history that brought the entire world to an abrupt and unexpected halt. Since the first reported case of the disease to date, the novel coronavirus has been able to wreak havoc in literary every corner of the globe and left an ever-growing number of unprecedented fatalities. The normal way of life has been disrupted, and the level of uncertainty about the end of this pandemic continues to manifest to many. Due to the urgency to bring this pandemic under control, medical officers have been able to recommend actions that people …

Multiple Frailty Model For Spatially Correlated Interval-Censored, Wanfang Zhang

Theses and Dissertations

In this paper, we consider the problem of multiple frailty selection for general interval-censored spatial survival data, which often occurs in clinical trials and epidemiological studies. The general interval-censored data is a mixture of left-, right- and interval-censored data. We propose a Bayesian semiparametric approach based on the Cox proportional hazard model, where monotone splines were used for non-parametrical modeling of the cumulative baseline hazards where the variable selection priors were used for frailty selection. A two-stage data augmentation with Poisson latent variables is developed for efficient computation. The approach is evaluated based a simulation study and illustrated using a …

Using Concurrent Functional Regression To Reconstruct River Stage Data During Flood Events And Identify Influential Functional Measurements, Ryan Pittman

Theses and Dissertations

On October 4, 2015, the Cedar Creek gage at Congaree National Park stopped reporting stages, and the readings did not resume until approximately two weeks later because of record-breaking rainfall that led to some of the worst flooding in South Carolina history. Our goal is to reconstruct the Cedar Creek stage during this missing two-week window. The Congaree River gage in Congaree National Park remained functioning throughout the October 2015 flood, when the stage reached its maximum recorded crest. The stages from the two gages are directly related during floods as water travels through the local spillways and flood planes …

Association Between The Beta Band Neural Response And The Behavioral Performance In Aphasic And Neurologically Intact Individuals, Yilun Zhang

Theses and Dissertations

The complex motor act of speech requires integrating linguistic and sensorimotor processes. Sensorimotor interaction mainly supports speech production in the form of state feedback control architecture. While speaking, subjects react to perturbations in the pitch of voice auditory feedback by changing their tone in the opposite direction to pitch-shift stimuli to compensate for the perceived pitch shift. Aphasia is a communication impairment affecting patients’ speaking, understanding, reading, and writing. The present study aims to examine the association between brain neural activity and the ability for speech auditory feedback error correction in both post-stroke aphasia and neurologically intact individuals. There are …

Marginally Interpretable Models And Multilevel Models For Quantile Regression With Random-Effects, Nahid Sultana Sumi

Theses and Dissertations

The quantile regression model is an active area of statistical research that has received a lot of attention. This complements the most widely used statistical tool, that is, mean regression analysis. Quantile regression analysis It has become more flexible because of its properties that include no assumption on the distribution of the response variable, equivalent to monotone transformations, and robustness to outliers. However, regression analysis offers methodological challenges if the observations are not independent. Cluster, multilevel, and repeated measures (longitudinal data) designs introduce such dependence. The correlation between observations on the same units or clusters should be accounted for to …

Bayesian Calibration Of The Icrp Zirconium Biokinetic Model And Use Of Canned Priors For The Evaluation Of Bioassay, Thomas Raymond Labone

Theses and Dissertations

The International Commission on Radiological Protection (ICRP) publishes biokinetic models that relate measurements of radioactive material in the body and excreta (bioassay) to the amount of the material taken into the body (intake). Given the intake and the biokinetic model, radiation dose to organs and tissues can be calculated. The ICRP approximates the biokinetics of radioactive materials in the body with compartmental models expressed mathematically as a system of ordinary differential equations, for which they provide point estimates of the rate constants. Inaccurate estimates of intake and radiation dose can result in cases where the biokinetics of an individual differ …

Correcting For Measurement Error In The Outcome When Estimating The Distribution Of Time To Pregnancy With The Current Duration Approach, Nicole Nasrallah

Theses and Dissertations

The current duration approach to modeling time-to-pregnancy (TTP) models the length of pregnancy attempt for women that are currently attempting pregnancy. There is a scarcity of studies, let alone TTP studies, that account for measurement error in the outcome. Previously, the benefits of a piecewise constant model with regards to bias in estimates of the survival function with measurement error and the parametric modelling of TTP was shown. In this thesis, correcting for measurement error in the outcome with the current duration approach is explored through piecewise constant models with log-normal measurement error. Five different methods are compared to determine …

Characterizing Convolutional Neural Network Early-Learning And Accelerating Non-Adaptive, First-Order Methods With Localized Lagrangian Restricted Memory Level Bundling, Benjamin O. Morris

Theses and Dissertations

This dissertation studies the underlying optimization problem encountered during the early-learning stages of convolutional neural networks and introduces a training algorithm competitive with existing state-of-the-art methods. First, a Design of Experiments method is introduced to systematically measure empirical second-order Lipschitz upper bound and region size estimates for local regions of convolutional neural network loss surfaces experienced during the early-learning stages. This method demonstrates that architecture choices can significantly impact the local loss surfaces traversed during training. Next, a Design of Experiments method is used to study the effects convolutional neural network architecture hyperparameters have on different optimization routines' abilities to …

Wavelet Methods For Very-Short Term Forecasting Of Functional Time Series, Jared K. Nystrom

Theses and Dissertations

Space launch operations at Kennedy Space Center and Cape Canaveral Space Force Station (KSC/CCSFS) are complicated by unique requirements for near-real time determination of risk from lightning. Lightning forecast weather sensor networks produce data that are noisy, high volume, and high frequency time series for which traditional forecasting methods are often ill-suited. Current approaches result in significant residual uncertainties and consequentially may result in forecasting operational policies that are excessively conservative or inefficient. This work proposes a new methodology of wavelet-enabled semiparametric modeling to develop accurate and timely forecasts robust against chaotic functional data. Wavelets methods are first used to …

Significant Gene Array Analysis And Cluster-Based Machine Learning For Disease Class Prediction, Myrine A. Barreiro-Arevalo

Theses and Dissertations

Gene expression analysis has been of major interest to biostatisticians for many decades. Such studies are necessary for the understanding of disease risk assessment and prediction, so that medical professionals and scientists alike may learn how to better create treatment plans to lessen symptoms and perhaps even find cures. In this study, we will investigate various gene expression analyses and machine learning techniques for disease class prediction, as well as assess predictive validity of these models and uncover differentially expressed (DE) genes for their relevant pathology datasets. Multiple gene expression datasets will be used to test model accuracies and will …

A Comparison Of Spatial Clustering Assessment Methods, Nadeesha Dilhani Vidanapathirana

Theses and Dissertations

Spatial clustering detection methods are widely used in many fields of research including sociology, epidemiology, ecology, and criminology. The objective of this study is to assess the performance of four spatial clustering detection methods: the average nearest neighbor ratio, Ripley’s K function, local Moran’s I and Getis-Ord Gi* statistics. We conduct a simulation study to evaluate the performance of each method for areal data under different types of spatial dependence and three different areal structures; a 20x20 regular grid, United States counties in six states and Canadian forward sortation areas (FSAs) in three provinces. The results shows that the empirical …

Accurate And Integrative Detection Of Copy Number Variants With High-Throughput Data, Xizhi Luo

Theses and Dissertations

Copy number variation, as a major source of genetic variation in the human genome, are gains or losses of the DNA segments. Copy number variation has gained considerable interest as it plays important roles in human complex diseases. Therefore, accurate detection of CNVs with data generated by modern genotyping technologies, such as SNP array and whole-exome sequencing (WES), comprises a critical step toward a better understanding of disease etiology. However, current statistical methodologies for CNV detection still face analytical challenges due to numerous genetic and technological factors that may lead to spurious findings. First, existing methods assume the independent observations …

Regression Methods For Group Testing Data, Michael Stutz

Theses and Dissertations

Group testing is an efficient method of disease screening, whereby individual specimens (e.g., blood, urine, etc.) are pooled together and tested as a whole for the presence of disease. A common goal is to use data arising from these testing protocols to better understand the relationship between disease status and potential risk factors (e.g., age, symptom status, etc.). Numerous statistical methodologies have been developed for this purpose, most of which are built within the framework of a generalized linear model. Recent authors have suggested the inadequacy of such regression methods to capture the true functional relationships when nonlinear effects are …

Statistically Defensible Wind Tunnel Models, Timothy A. Roche

Theses and Dissertations

Wind tunnels are used to test scale-model air frames in order to collect aerodynamic data. The Subsonic Aerodynamic Research Laboratory (SARL) Wind Tunnel is a low speed wind tunnel located at Wright-Patterson Air Force Base. The SARL Wind Tunnel team approached AFIT for assistance in creating statistically defensible models for the conditions inside the wind tunnel. During a wind tunnel test, pressure sensors cannot be placed at the test model. Instead, pressure is measured by a pitot probe permanently mounted in the corner of the test chamber. The pressure at the model location is predicted from the measurements taken by …

Stock Markets Performance During A Pandemic: How Contagious Is Covid-19?, Yara Abushahba

Theses and Dissertations

Background and Motivation: The coronavirus (“COVID-19”) pandemic, the subsequent policies and lockdowns have unarguably led to an unprecedented fluid circumstance worldwide. The panic and fluctuations in the stock markets were unparalleled. It is inarguable that real-time availability of news and social media platforms like Twitter played a vital role in driving the investors’ sentiment during such global shock.

Purpose:The purpose of this thesis is to study how the investor sentiment in relation to COVID-19 pandemic influenced stock markets globally and how stock markets globally are integrated and contagious. We analyze COVID-19 sentiment through the Twitter posts and investigate its …

Statistical Analysis Of A Joint Stochastic Model For Recurrent Competing Risks, Longitudinal Marker, And Health Status, Lili Tong

Theses and Dissertations

Joint modeling approach has been applied in many applications in biomedical, reliability, and social-economic research. For example, in clinical trials and medical research, different kinds of patient information are gathered over time, such as recurrent competing risk events (e.g., relapses of different types of tumor), longitudinal marker (e.g., tumor size), and health status (e.g., if a patient is dead or not). These data are usually correlated, joint models enable the analysis of these correlated data. This dissertation proposes a class of joint dynamic models for simultaneously modeling the three types of processes: a recurrent competing risk (RCR) process, a health …

Improving Failure Mode & Effect Analysis ( Fmea ) Method Using Discrete Event Simulation, Adil Abdukeyum

Theses and Dissertations

To improve system performances and process dependability, analyzing the system accurately is an essential step but difficult to achieve and it is even more challenging if the system is complex and dynamic. A popular tool called FMEA has been widely used to analyze and improve systems. However, both academia and industry acknowledge its subjectivity and lack of cause-effect analysis capability. Therefore, in this research, the author presents a more objective and data-driven method called Discrete Event Simulation to improve FMEA’s analysis capability. Also, how the Discrete Event Simulation may enhance the FMEA by a step-by-step analysis approach is presented by …

Bayesian Nonparametric Model For Functional Data Analysis, Tahmidul Islam

Theses and Dissertations

Functional data analysis (FDA) experienced a burst of growth after Ramsay and Silverman published their textbook in 1997. Functional data analysis interests researchers because of the challenges it adds to well-established multivariate analysis. Unlike finite dimensional random vectors, we visualize infinite dimensional random functions; for example, curves, images, brain scans, etc. A vast amount of literature have been dedicated to developing models for functional data. The ideas are mostly based on basis function representations and kernel-based nonparametric methods. In this dissertation, we propose a Bayesian treatment of nonparametric functional data analysis by introducing a Gaussian process (GP) over the space …

Bayesian Methods In Analyzing The Association Of Random Variables, Zichen Ma

Theses and Dissertations

This dissertation focuses on studying the association between random variables or random vectors from the Bayesian perspective. In particular, it consists of two topics: (1) hypothesis testing for the independence among groups of random variables; and (2) modeling the dynamic association between two random variables given covariates.

In Chapter 2, a nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor …

A Simulation-Based Study Of Location-Shift Models Under Non-Normal Conditions, Ummay Khayrunnesa Anika

Theses and Dissertations

In this study, we compare ordinary least squares (OLS), generalized least squares (GLS), M- and quantile regression (QR) estimators for a continuous response variable under different scenarios by conducting a simulation study. We assess the performance of the estimators in terms of bias, average distance, mean squared error, coverage probability, and ratio of estimated standard error and empirical standard deviation. OLS estimator performs the best when the errors are homoscedastic normal or homoscedastic but skewed (exponential) having no outliers. GLS estimator shows good comparative results to QR when the errors are heteroscedastic normal or heteroscedastic heavy-tailed (t-distributed). The most satisfactory …

An Examination Of Civilian Retention In The United States Air Force, William F. Wilson

Theses and Dissertations

The backbone of the United States Air Force is undoubtedly the large civilian workforce that supplements the great work that is accomplished. Many research studies have been conducted on officer and enlisted personnel to ensure that the career fields are properly developed and managed to meet the ever growing demands of the military's varied missions, but no recent studies have focused on the civilian workforce. Striking a balance between new and experienced employees is paramount to success given the ever-changing economic and political landscapes where we find ourselves. The first part of the research uses logistic regression to determine the …

Analysis Of Functional Responses In Experimental Design, Matthew E. Scherer

Theses and Dissertations

The growth of sensor streamed data in recent years increases the demand for an analytical technique to properly address data measured continuously. The design and analysis of experiments (DOE) of U.S. Air Force assets are based off of sensor streamed data. Functional data analysis (FDA) is an approach of analyzing data existing over a continuum. This research aids in filling the intersection of FDA and DOE by examining a case study of an experimental design with a functional response in addition to insight on software capabilities in FDA. The case study considers a functional linear model of a whole-plot from …

The Wargaming Commodity Course Of Action Automated Analysis Method, William T. Deberry

Theses and Dissertations

This research presents the Wargaming Commodity Course of Action Automated Analysis Method (WCCAAM), a novel approach to assist wargame commanders in developing and analyzing courses of action (COAs) through semi-automation of the Military Decision Making Process (MDMP). MDMP is a seven-step iterative method that commanders and mission partners follow to build an operational course of action to achieve strategic objectives. MDMP requires time, resources, and coordination – all competing items the commander weighs to make the optimal decision. WCCAAM receives the MDMP's Mission Analysis phase as input, converts the wargame into a directed graph, processes a multi-commodity flow algorithm on …

Optimizing Critical Values And Combining Axes For Multi-Axial Neck Injury Criteria, Ethan J. Gaston

Theses and Dissertations

The Air Force employs ejection seats in its high-performance aircraft. While these systems are intended to ensure aircrew safety, the ejection process subjects the aircrew to potentially injurious forces. System validation includes evaluation of forces against a standard which is linked to the probability of injury. The Muti-Axial Neck Injury Criteria (MANIC) was developed to account for forces in all six degrees of freedom. Unfortunately, the MANIC is applied to each of the three linear input directions separately and applies different criterion values for each direction. These three separate criteria create a lack of clarity regarding acceptable neck loading, leading …

Behavior Of Lightning In Developing Storms, Erick A. Tello

Theses and Dissertations

Air Force weather squadrons issue a warning when lightning activity is observed within 5 nautical miles (NM) of protected areas. Upon receiving this warning, personnel outdoors are expected to pause work and move inside. Studies sponsored by the 45th Weather Squadron (45 WS) have concluded that the 5 NM warning radius can be safely reduced for well-developed storms. This thesis investigates whether radii for storms in early development can also be reduced. Our research develops algorithms to partition lightning sensor data into storms. Next, storms are filtered to their earliest lightning events, and the study calculates distances between successive early …

The Determinations Of Public Trust In The Government Of Egypt: An Empirical Study, Mohamed Elimam

Theses and Dissertations

Trust is a concept that is usually studied in the context of social interactions. At varying levels, we trust our families and friends, we trust strangers who share some traits with us and even trust institutions like banks with our savings and to handle our personal finances. By expansion, political trust, or the public's trust in government as a whole and as individual agencies. Trust in government forms a basis for the legitimacy. High levels of political trust facilitates the implementation of policies with more willing compliance from the public. This is more evident in situations like global and national …

Statistical Approaches For Estimation And Comparison Of Brain Functional Connectivity, Jifang Zhao

Theses and Dissertations

Drug addiction can lead to many health-related problems and social concerns. Functional connectivity obtained from functional magnetic resonance imaging (fMRI) data promotes a variety of fundamental understandings in such association. Due to its complex correlation structure and large dimensionality, the modeling and analysis of the functional connectivity from neuroimage are challenging. By proposing a spatio-temporal model for multi-subject neuroimage data, we incorporate voxel-level spatio-temporal dependencies of whole-brain measurements to improve the accuracy of statistical inference. To tackle large-scale spatio-temporal neuroimage data, we develop a computationally efficient algorithm to estimate the parameters. Our method is used to identify functional connectivity and …

Topics In Design And Analysis Of Experiments: Calibration, Sequential Experimentation, And Model Selection, Christine Miller

Theses and Dissertations

Experiments are widely used across multiple disciplines to uncover information about a system or processes. Experimental design is a statistical technique devoted to the methodology of selecting the appropriate samples to aid in the subsequent analysis. We research three open problems in experimental designs regarding calibration, sequential experimentation, and model selection. First, we focus on calibration; the impact of experimental design choice on the performance of statistical calibration is largely unknown. We investigate the performance of several experimental designs with regards to inverse prediction via a comprehensive simulation study. Specifically, we compare several design types including traditional response surface designs, …

Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones

Theses and Dissertations

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a …

Methods For Developing A Machine Learning Framework For Precise 3d Domain Boundary Prediction At Base-Level Resolution, Spiro C. Stilianoudakis

Theses and Dissertations

High-throughput chromosome conformation capture technology (Hi-C) has revealed extensive DNA looping and folding into discrete 3D domains. These include Topologically Associating Domains (TADs) and chromatin loops, the 3D domains critical for cellular processes like gene regulation and cell differentiation. The relatively low resolution of Hi-C data (regions of several kilobases in size) prevents precise mapping of domain boundaries by conventional TAD/loop-callers. However, high resolution genomic annotations associated with boundaries, such as CTCF and members of cohesin complex, suggest a computational approach for precise location of domain boundaries.

We developed preciseTAD, an optimized machine learning framework that leverages a random …