Statistics and Probability Commons^™

Bivariate Generalization Of The Time-To-Event Conditional Reassessment Method With A Novel Adaptive Randomization Method, Donglin Yan

Theses and Dissertations--Epidemiology and Biostatistics

Phase I clinical trials in oncology aim to evaluate the toxicity risk of new therapies and identify a safe but also effective dose for future studies. Traditional Phase I trials of chemotherapies focus on estimating the maximum tolerated dose (MTD). The rationale for finding the MTD is that better therapeutic effects are expected at higher dose levels as long as the risk of severe toxicity is acceptable. With the advent of a new generation of cancer treatments such as the molecularly targeted agents (MTAs) and immunotherapies, higher dose levels no longer guarantee increased therapeutic effects, and the focus has shifted …

Improved Standard Error Estimation For Maintaining The Validities Of Inference In Small-Sample Cluster Randomized Trials And Longitudinal Studies, Whitney Ford Tanner

Theses and Dissertations--Epidemiology and Biostatistics

Data arising from Cluster Randomized Trials (CRTs) and longitudinal studies are correlated and generalized estimating equations (GEE) are a popular analysis method for correlated data. Previous research has shown that analyses using GEE could result in liberal inference due to the use of the empirical sandwich covariance matrix estimator, which can yield negatively biased standard error estimates when the number of clusters or subjects is not large. Many techniques have been presented to correct this negative bias; However, use of these corrections can still result in biased standard error estimates and thus test sizes that are not consistently at their …

Using Prescription Drug Monitoring Data To Inform Population Level Analysis Of Opioid Analgesic Utilization, Huong T. T. Luu

Theses and Dissertations--Epidemiology and Biostatistics

Increased opioid analgesic (OA) prescribing has been associated with increased risk of prescription opioid diversion, misuse, and abuse. States established prescription drug monitoring programs (PDMPs) to collect and analyze electronic records for dispensed controlled substances to reduce prescription drug abuse and diversion. PDMP data can be used by prescribers for tracking patient’s history of controlled substance prescribing to inform clinical decisions.

The studies in this dissertation are focused on the less utilized potential of the PDMP data to enhance public health surveillance to monitor OA prescribing and co-prescribing and association with opioid overdose mortality and morbidity. Longitudinal analysis of OA …

Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

No abstract provided.

When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik

Mathematics Faculty Publications

We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, …

Using Data Mining To Model Student Achievement On The 4th Grade Timss 2015 Mathematics Assessment: A Five Nation Sudy, Annette M. Siemssen

Open Access Theses & Dissertations

Data mining has been successfully used by financial and retail companies since the mid-1960's to create predictive models and reveal unexpected relationships. However, it remains underutilized as a tool in educational research. Large-scale standardized assessment programs such as the Trends in International Mathematics and Science Study (TIMSS) provide vast amounts of data with the potential for providing new insights in education. Five nations, the Republic of Korea, the United States, Germany, Kuwait, and Kazakhstan were selected based on General Response Style theory to represent a spectrum of cultural backgrounds, from acquiescent to midpoint to individualistic (Hastedt, D. & van de …

Estimating The Optimal Cutoff Point For Logistic Regression, Zheng Zhang

Open Access Theses & Dissertations

Binary classification is one of the main themes of supervised learning. This research is concerned about determining the optimal cutoff point for the continuous-scaled outcomes (e.g., predicted probabilities) resulting from a classifier such as logistic regression. We make note of the fact that the cutoff point obtained from various methods is a statistic, which can be unstable with substantial variation. Nevertheless, due partly to complexity involved in estimating the cutpoint, there has been no formal study on the variance or standard error of the estimated cutoff point.

In this Thesis, a bootstrap aggregation method is put forward to estimate the …

Hierarchical Multiplicity Control Methods For Linear Models, Dimuthu Dilshan Fernando

Open Access Theses & Dissertations

HypoThesis testing is a commonly used statistical inference technique on which a statement of the population is investigated through the evidence from a representative sample of the population. With simultaneous testing of more than one null hypotheses need for an appropriate multiple comparison method is essential. With motivation from the study of Bogomolov et al. (2017) we have modified a multiple comparison tree structure to build the required comparisons and focus on controlling the FWER (Family Wise Error Rate) using the Bonferroni procedure. The proposed method has advantages such as controlling the global error rates separately at each level, families …

Backward Elimination Algorithm For High Dimensional Variable Screening, Sophia Korkor Foli

Open Access Theses & Dissertations

In recent times, variable selection in high-dimensional data has become a challenging prob- lem. We investigate here a popular but classical variable screening method, the Back- ward Elimination (BE) in a high dimensional setup (small-n-large P). The BE method as a variable screening method reduces the dimension of small-n-large P data into a lower dimensional data and then established shrinkage methods such as: LASSO, SCAD and MCP can be applied directly. To overcome the problems in high dimensional data, Chen and Chen (2008) recently developed a family of Extended Bayesian Information Criterion (EBIC) which is consistent with finite sample properties …

Extraction Of Fiber Morphology From Sem Images For Quality Control Of Fiber Reinforced Composites Manufacturing, Md Fashiar Rahman

Open Access Theses & Dissertations

The morphology of fibers (e.g. spatial uniformity, orientation, and length) plays a decisive role in determining the material properties or fabrication quality of fiber-reinforced nanocomposites. Hence, determining the morphology becomes a very critical issue in the field of nanocomposite quality control. The conventional way of quality inspection is to take the scanning electron microscopic (SEM) images of the cross-section of composite material and do the visual checking of these SEM images to evaluate the nanofiber alignment and length distribution. But this type of inspection is often subjective, inaccurate and time consuming. Moreover, the extremely small size of nanofibers makes the …

Matroid - Based Variable Selection For Complex Data Structures, Wimarsha Thathsarani Jayanetti

Open Access Theses & Dissertations

This research project has the objective to extend use of the matroid algorithm using statistically based criteria, Joint/Multivariate Cumulants (Speed, 1983) and Effective Dependence (Pena & Rodriguez, 2003) to capture linear as well as non-linear higher order dependencies. We also improve variable selection for complex data structures using the proposed matroid algorithm. The limiting distribution of the joint cumulant was defined using U-statistics theory by Hoeffding (1948). U-statistics variance as theorized by Hoeffding provide a lower bound for the estimated variance, and our simulation results justify the use of Hoeffding U-statistic variance for determining a threshold for joint cumulants deviation …

Approximation Of Quantiles Of Rank Test Statistics Using Almost Sure Limit Theorems, Mark Ledbetter

Mathematics & Statistics Theses & Dissertations

There are many problems in statistics where the analysis is based on asymptotic distributions. In some cases, the asymptotic distribution is in an open form or is intractable. One possible solution is the logarithmic quantile estimation (LQE) method introduced by Thangavelu (2005) for rank tests and Fridline (2010) for the correlation coefficient. LQE is derived from an almost sure version of the central limit theorem using the results of Berkes and Csaki (2001), and it estimates the quantiles of a test statistic using only the data. To date, LQE has been used in only a few applications. We extend the …

Adaptive Methods For Point Cloud And Mesh Processing, Zinat Afrose

Computational Modeling & Simulation Engineering Theses & Dissertations

Point clouds and 3D meshes are widely used in numerous applications ranging from games to virtual reality to autonomous vehicles. This dissertation proposes several approaches for noise removal and calibration of noisy point cloud data and 3D mesh sharpening methods. Order statistic filters have been proven to be very successful in image processing and other domains as well. Different variations of order statistics filters originally proposed for image processing are extended to point cloud filtering in this dissertation. A brand-new adaptive vector median is proposed in this dissertation for removing noise and outliers from noisy point cloud data.

The major …

Analyzing Sensor Based Human Activity Data Using Time Series Segmentation To Determine Sleep Duration, Yogesh Deepak Lad

Masters Theses

"Sleep is the most important thing to rest our brain and body. A lack of sleep has adverse effects on overall personal health and may lead to a variety of health disorders. According to Data from the Center for disease control and prevention in the United States of America, there is a formidable increase in the number of people suffering from sleep disorders like insomnia, sleep apnea, hypersomnia and many more. Sleep disorders can be avoided by assessing an individual's activity over a period of time to determine the sleep pattern and duration. The sleep pattern and duration can be …

Engaging Students In The Practice Of Statistics Through Undergraduate Research, Debra L. Hydorn

Mathematics Articles

As statisticians, we engage in a variety of activities, some of which are regularly integrated into our undergraduate courses. However, the individual courses that comprise a mathematics or statistics degree program might not provide students with experiences in the broader range of activities that define the practice of statistics. To remedy this situation, faculty can consider developing and mentoring undergraduate research projects. This article briefly discusses the skills that comprise statistical practice along with some course and program options for helping students to develop these skills. Then, types of undergraduate research projects in statistics are described to help faculty generate …

Statistical Methods For Detecting Causal Rare Variants And Analyzing Multiple Phenotypes, Xinlan Yang

Dissertations, Master's Theses and Master's Reports

This dissertation includes two papers with each distributed in one chapter. To date, genome-wide association studies (GWAS) have identified a large number of common variants that are associated with complex diseases successfully. However, the common variants identified by GWAS only account for a small proportion of trait heritability. Many studies showed that rare variants could explain parts of the missing heritability. Since the well-developed common variant detecting methods are underpowered for rare variant association tests unless sample sizes or effect sizes are very large, investigation the roles of rare variants in complex diseases presents substantial challenges. In chapter 1, we …

Statistical Methods For Analyzing Multivariate Phenotypes And Detecting Rare Variant Associations, Huanhuan Zhu

Dissertations, Master's Theses and Master's Reports

This dissertation includes four papers with each distributed in one chapter.

In chapter 1, I compared the performance of eight multivariate phenotype association tests. The motivation to conduct this power comparison paper is as follows. For nearly 15 years, genome-wide association studies (GWAS) have been widely used to identify genetic variants associated with human diseases and traits. GWAS typically investigate genetic variants for a predefined phenotype, thus fail to identify weak but important effects. In recent years, many multivariate association tests have been developed. However, there is a lack of comprehensive summary of such kinds of approaches. To fill this …

Offline And Online Density Estimation For Large High-Dimensional Data, Aref Majdara

Dissertations, Master's Theses and Master's Reports

Density estimation has wide applications in machine learning and data analysis techniques including clustering, classification, multimodality analysis, bump hunting and anomaly detection. In high-dimensional space, sparsity of data in local neighborhood makes many of parametric and nonparametric density estimation methods mostly inefficient.

This work presents development of computationally efficient algorithms for high-dimensional density estimation, based on Bayesian sequential partitioning (BSP). Copula transform is used to separate the estimation of marginal and joint densities, with the purpose of reducing the computational complexity and estimation error. Using this separation, a parallel implementation of the density estimation algorithm on a 4-core CPU is …

Application Of Remote Sensing And Machine Learning Modeling To Post-Wildfire Debris Flow Risks, Priscilla Addison

Dissertations, Master's Theses and Master's Reports

Historically, post-fire debris flows (DFs) have been mostly more deadly than the fires that preceded them. Fires can transform a location that had no history of DFs to one that is primed for it. Studies have found that the higher the severity of the fire, the higher the probability of DF occurrence. Due to high fatalities associated with these events, several statistical models have been developed for use as emergency decision support tools. These previous models used linear modeling approaches that produced subpar results. Our study therefore investigated the application of nonlinear machine learning modeling as an alternative. Existing models …

Wildfire Emissions In The Context Of Global Change And The Implications For Mercury Pollution, Aditya Kumar

Dissertations, Master's Theses and Master's Reports

Wildfires are episodic disturbances that exert a significant influence on the Earth system. They emit substantial amounts of atmospheric pollutants, which can impact atmospheric chemistry/composition and the Earth’s climate at the global and regional scales. This work presents a collection of studies aimed at better estimating wildfire emissions of atmospheric pollutants, quantifying their impacts on remote ecosystems and determining the implications of 2000s-2050s global environmental change (land use/land cover, climate) for wildfire emissions following the Intergovernmental Panel on Climate Change (IPCC) A1B socioeconomic scenario.

A global fire emissions model is developed to compile global wildfire emission inventories for major atmospheric …

An Analysis Of Equity-Linked Insurance Pricing, Clara C. Ortgies

Honors Program Theses

This comprehensive study of equity-linked insurance options will explore the pricing of certificates of deposit and life insurance options using a present value method. With this study, I will be able to construct and price various equity-linked insurance products, with a focus on life insurance, that insurance companies could then sell to prospective customers. I will use concepts and formulas based in actuarial math, probability theory, and financial engineering in order to construct, price, and analyze new equity-linked insurance products. The fundamental methodology I will use involves applying pricing theory based on the expected value of the insurance payoff present …

A Land Use Regression Model For Explaining Spatial Variation In Air Pollution Levels Using A Wind Sector Based Approach, Owen Naughton, Aoife Donnelly, Paul Nolan, Francesco Pilla, Bruce Misstear, Brian Broderick

Articles

Estimating pollutant concentrations at a local and regional scale is essential for good ambient air quality information in environmental and health policy decision making. Here we present a land use regression (LUR) modelling methodology that exploits the high temporal resolution of fixed-site monitoring (FSM) to produce viable air quality maps. The methodology partitions concentration time series from a national FSM network into wind-dependent sectors or “wedges”. A LUR model is derived using predictor variables calculated within the directional wind sectors, and compared against the long-term average concentrations within each sector. This study demonstrates the value of incorporating the relative position …

Accumulating Evidence Of The Impact Of Voter Id Laws: Student Engagement In The Political Process, Kelly Mcconville, L. Stokes, M. Gray

Mathematics & Statistics Faculty Works

Recently, voter ID laws have been instituted, modified or overturned in many states in the US. As these laws change, it is important to have accurate measures of their impact. We present the data collection methods and results of class projects that attempted to quantify the impact of the voter ID laws in areas of three states. We also summarize the types of data used to assess the impact of voter ID laws and discuss how our data address some of the shortcomings of the usual techniques for assessing the impact of voter ID laws.

Unmasking Cost Growth Behavior: A Longitudinal Study, Cory N. D'Amico, Edward D. White, Jonathan D. Ritschel, Scott R. Kozlak

Faculty Publications

This article examines how cost growth factors (CGF) change over a program’s acquisition life cycle for 36 Department of Defense aircraft programs. Starting from Milestone B, the authors examine CGFs at five gateways: Critical Design Review, First Flight (FF), the end of Developmental Test and Evaluation (DT&E), Initial Operational Capability, and Full Operational Capability. Each CGF is assigned a color rating based upon the program’s cost growth: Green (low), Amber (moderate), or Red (high). Significant findings include dependencies among similar CGF color ratings and cost growth occurring primarily between FF and the end of DT&E during a program’s life cycle.

Spatial Modelling And Wildlife Health Surveillance: A Case Study Of White Nose Syndrome In Ontario, Lauren Yee

Theses and Dissertations (Comprehensive)

Wildlife data is often limited by survey effort, small sample sizes, and spatial biases associated with collection and missing data. These factors can create unique challenges from a surveillance perspective when trying to extract spatial patterns of habitat suitability and disease distributions for conservation and management purposes. This thesis examined data quality from a wildlife health database in the context of spatial analysis of wildlife disease. Spatial analysis of the data to predict habitat suitability of bats and white nose syndrome afflicted bats was examined by using the MaxEnt modelling method. Methods to reduce spatial bias were examined and specific …

A Primer On Noise-Induced Transitions In Applied Dynamical Systems, Eric Forgoston, Richard O. Moore

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic …

A Rotatable Asymmetric Variable Compensation Mirt Model, Xinchu Zhao

Theses and Dissertations

The purpose of this study is to develop, estimate, and interpret a new variable compensation multidimensional item response theory (MIRT) model, named the Rotatable Asymmetric Variable Compensation Model (RAVCM), that allows for transformation between different correlation structures. Since the model is rotatable like the common compensatory models (CM), it is not necessary to specify or estimate the correlation of abilities to recover the model. Also, it can approximate the existing MIRT models well. In simulation, the RAVCM is shown to estimate the parameters with small error, especially when the non-compensatory model (NCM) is the true model and the correlation of …

Netnographic Slog: Creative Elicitation Strategies To Encourage Participation In An Online Community Of Practice For Early Education And Care, Ruth Wallace

Research outputs 2014 to 2021

Active, participatory netnography, in contrast to passive netnography, is essential if researchers are to gain rich rewards from the rigorous collection of qualitative data. However, researchers should be aware of the ‘netnographic slog’; “the blood, sweat and tears” associated with eliciting quality data and encouraging active participation in online communities.

This article examines the – Supporting Nutrition for Australian Childcare (SNAC) – online community of practice, established to support healthy eating practices in early childhood education and care settings. To ensure research rigour, Kozinets’ netnographic steps were employed. Garnering member participation in this online community was a slog; most community …

Multiclass Classification Using Support Vector Machines, Duleep Prasanna W. Rathgamage Don

College of Graduate Studies: Theses & Dissertations

In this thesis, we discuss different SVM methods for multiclass classification and introduce the Divide and Conquer Support Vector Machine (DCSVM) algorithm which relies on data sparsity in high dimensional space and performs a smart partitioning of the whole training data set into disjoint subsets that are easily separable. A single prediction performed between two partitions eliminates one or more classes in a single partition, leaving only a reduced number of candidate classes for subsequent steps. The algorithm continues recursively, reducing the number of classes at each step until a final binary decision is made between the last two classes …

Developing, Piloting, And Factor Analysis Of A Brief Survey Tool For Evaluating Food And Composting Behaviors: The Short Composting Survey, Jennie Norton

All Master's Theses

Composting on a university campus may take a variety of forms. Sustainable approaches to waste management can be taught and supported through educational programs, peer-to-peer behavior modeling, and composting program interventions. Although peer-reviewed research on composting interventions is somewhat lacking, student interest in the topic is demonstrated by a range of exploratory senior projects and pilot interventions conducted at colleges across the United States and abroad. The purpose of this study was twofold: conduct an educational compost intervention pilot study and develop a survey tool to measure participant attitudes surrounding food behaviors and composting. The Compost Project pilot study focused …