Statistics and Probability Commons^™

Improvement And Evaluation Of Multiple Imputation By Heckman's One-Step Mle For Binary Mnar Outcomes And Various Types Of Mar Covariates, Xin W. Shore

Mathematics & Statistics ETDs

Missing data is inevitable in clinical epidemiology. It becomes one of the major challenges in the analyses and can potentially undermine the validity of results and conclusions. Although methods for handling missing data with mechanisms of missing completely at random (MCAR) or missing at random (MAR) have been widely researched, methods adapted for the missing not at random (MNAR) mechanism are less studied. Galimard et al. (2018) have derived a method to use multiple imputation by Heckman's One-Step ML Estimation for binary MNAR outcome and continuous MAR covariates (MIHEml). This dissertation focuses on updating MIHEml in terms of …

Assessing The Adequacy Of A Prediction Model, Abhaya Indrayan, Sakshi Mishra Ms

COBRA Preprint Series

No abstract provided.

Effect Of Correlation Boundaries On Collinearity And Bias In Ordinary Least Square Regression, Yumo Xue

All ETDs from UAB

Linear regression (LM) stands as one of the prevailing methods used to assess the association between a dependent variable and independent variables, typically estimated using ordinary least squares. However, this approach frequently faces obstacles when applied to biomedical data, due to the issue of correlated independent variables (collinearity). Collinearity is a potential issue in observational studies, where researchers might omit less significant correlated variables from their model. This is often guided by the rule of thumb that a Variance Inflation Factor (VIF) of 10 indicates severe collinearity. Our hypothesis is that relying on this rule of thumb is arbitrary, and …

Supplementary Files For: Quantifying The Impact Of Rain-On-Snow Induced Flooding In The Western United States, Emma Watts, Brennan Bean

Browse all Datasets

Serious flooding can happen when rain falls on snow, which we call a rain-on-snow (ROS) event. Increasing our understanding of the behavior of floods resulting from ROS events can help us design better systems to manage flood water and prevent it from causing damage. This thesis explores how ROS events affect streamflow in the Western United States by examining the weather conditions that precede a streamflow surge. We classify stream surges as ROS or non-ROS induced based on these weather conditions, which helps us separate floods caused by ROS events from those caused by other factors. By comparing these different …

Review Of Fluke: Chance, Chaos, And Why Everything We Do Matters, Walter Hill

The Journal of Social Encounters

No abstract provided.

Pooling And Winsorizing Machine Learning Forecasts To Predict Stock Returns With High-Dimensional Data, Erik Mekelburg, Jack Strauss

Finance: Faculty Scholarship

We evaluate US market return predictability using a novel data set of several hundred ag- gregated firm-level characteristics. We apply LASSO, Elastic Net, Random Forest, Neural Net, Extreme Gradient Boosting, and Light Gradient Boosting Machine methods and find these models experience large prediction errors that lead to forecast failures. However, winsorizing and pooling machine learning model forecasts provides consistent out-of-sample predictability. To assess robustness, we apply machine learning methods to high-dimensional data for Canada, China, Germany and the UK as well as the Goyal-Welch data. All machine learning models we consider, except for the ensemble pooled methods, fail to significantly …

Generalized Periodicity And Applications To Logistic Growth, Martin Bohner, Jaqueline Mesquita, Sabrina Streipert

Mathematics and Statistics Faculty Research & Creative Works

Classically, a continuous function f:R→R is periodic if there exists an ω>0 such that f(t+ω)=f(t) for all t∈R. The extension of this precise definition to functions f:Z→R is straightforward. However, in the so-called quantum case, where f:qN0→R (q>1), or more general isolated time scales, a different definition of periodicity is needed. A recently introduced definition of periodicity for such general isolated time scales, including the quantum calculus, not only addressed this gap but also inspired this work. We now return to the continuous case and present the concept of ν-periodicity that connects these different formulations of periodicity for …

The Cubic-Quintic Nonlinear Schrödinger Equation With Inverse-Square Potential, Alex H. Ardila, Jason Murphy

Mathematics and Statistics Faculty Research & Creative Works

We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.

Analysis Of Data Containing Outliers, David L. Farnsworth

Articles

A strategy for accommodating outlying observations, as well as non-representative, suspect, missing, or otherwise troubling observations, is described. Each unusual observation is decomposed into the sum of two components. One component is the value implied by the trusted observations in the data set. The other component is the unusual part. In this way, the fitting of the data set can then proceed, and, additionally, a numerical value can be ascribed to the unusual part. The method offers not only an antidote for observations with irregular numerical values, which often have the power to contaminate and alter analyses, but also a …

Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …

Multi-Label Classification Using Conformal Prediction, Chhavi Tyagi

Dissertations

In many machine learning applications, such as image tagging, document classi-fication, and medical diagnosis, a data instance can be associated with multiple classes in parallel so that each instance is associated with multiple response variables simultaneously defining multi-label classification. Standard multi-label classification methods that provide point predictions have been developed. They lack in quantifying the uncertainty of predictions. These methods also lack in accounting for label dependencies and are very computationally expensive. This dissertation develops two methods of multi-label classification using conformal prediction that quantify the uncertainty of predictions. Chapter 1 introduces notations and tools that have been used in …

Large Deviation Theory In Stochastic Processes: Applications To Biological Modeling, Moshe C. Silverstein

Dissertations

This dissertation delves into developing and applying stochastic models to analyze complex biological systems. It leverages Large Deviation Theory (LDT) to gain insights into these systems, focusing on two key examples: neural networks and calcium signaling dynamics. Traditional deterministic methods frequently fail to capture biological processes' randomness and inherent variability. Meanwhile, many stochastic approaches struggle to be mathematically tractable or provide accessible insights. The approach introduced in this study provides rigorous mathematical frameworks to enhance understanding of these stochastic behaviors while remaining tractable and insightful.

A stochastic model for a random biological neural network is constructed that addresses the dependencies …

Investigating Mixed Effects Random Forest Models In Predicting Satisfaction With Online Learning In Higher Education, Jiaqi (Jackie) Shi

Electronic Theses and Dissertations

One of the many impacts of the COVID-19 pandemic has been the increasing prevalence and accessibility of online education. This trend has also introduced challenges for students, instructors, and institutions. This study examines factors affecting online course satisfaction, focusing on individual, instructor, and institutional level characteristics with clustered, separated train and test datasets across two terms. This study compares Hierarchical Linear Model (HLM), Non-clustered and Clustered Random Forest (RF & MERF) models to understand these impacts. This intention is to provide a comprehensive framework comparing traditional HLM with the latest developed MERF models while delving into the effectiveness of RF …

The Naked Truth Of My Voice: Surveying The Soul Of An Aspiring Educator From Dusk To Dawn: An Arts-Based Auto-Criticism Inquiry, Siddharth Maan

Electronic Theses and Dissertations

This dissertation is based on auto-criticism, a new qualitative inquiry that combines educational criticism and arts-based research. It focuses on my own experiences as an aspiring educator who struggles with stuttering and public speaking anxiety. The study aims to describe, interpret, evaluate, and thematize my experiences of dealing with public speaking anxiety and stuttering before, during, and after classroom teaching. In addition, this dissertation highlights the potential contributions of auto-criticism as a methodology to qualitative research and higher education. I utilized journaling to document data. Photos and music were also used to enhance the understanding of my lived experiences and …

Investigating Servant Leadership Measurement: A Mixed-Methods Study Integrating Content Analysis And Meta-Analysis, Kai Torsten Schramm

Electronic Theses and Dissertations

This study aimed to understand the similarities and differences among servant leadership measures and the variations in their effect sizes on job performance and job satisfaction. This paper explores how the items in servant leadership measures portrayed the servant leadership construct and how these relate to the outcomes. The researcher used an exploratory sequential mixed methods design. Which involved a qualitative content analysis of the measurement items and a meta-analysis of outcomes, considering the findings from the content analysis. Six key categories determined the three main themes: selfless generosity, inspiring influence, adaptive humility, integrity, empowering, and harmonious engagement. The three …

Exploration Of Positive Deviance In Prevention Of Underweight In The Under-Five: A Qualitative Study On Low-Income Urban Families, Irwan Budiono, Lukman Fauzi, Dewi Sari Rochmayani

Kesmas

Children under the age of five (the under-five) from low-income families are more vulnerable to experience underweight. This nutritional vulnerability is evident in the preliminary study, where 35.1% of the under-five experience underweight, and 28.48% are low-income families. This study aimed to explore Positive Deviance (PD) behaviors in preventing underweight among the under-five. The study applied a qualitative approach with a case study design. Data collection took place in July-August 2022, focusing on low-income families in the Gunung Brintik area. Data were collected through two focus group discussions, seven in-depth interviews, and five key informant interviews. Coding, subtheme, and theme …

Risk Factors For Cognitive Impairment In Adult Population Of Coastal Area: A Cross-Sectional Study In Maringkik Island, Indonesia, Herpan Syafii Harahap, Arina Windri Rivarti, Nurhidayati Nurhidayati, Fitriannisa Faradina Zubaidi, Dini Suryani, Legis Ocktaviana Saputri, Yanna Indrayana, Athalita Andhera, Muhammad Hilam, Abiyyu Didar Haq

Kesmas

Cognitive impairment is a medical condition commonly found in elderly populations, which can be due to vascular risk factors in patients. There remains limited data on risk factors for cognitive impairment among coastal region populations. This study aimed to investigate risk factors for cognitive impairment in the adult population of Maringkik Island, West Nusa Tenggara Province, Indonesia. Data collected were age, sex, education level, hypertension, antihypertensive treatment, diabetes mellitus, cigarette smoking, and body mass index status. A total of 114 participants were recruited using a consecutive sampling method. The participants’ cognitive function assessment used the Mini-Cog instrument. The cognitive impairment …

Variation And Predictors Of Covid-19 Mortality In Hospitalized Cases In West Sumatra Province, Indonesia: A Retrospective Observational Study, Defriman Djafri, Ade Suzana Eka Putri, Yudi Pradipta

Kesmas

During 2020, the year of the COVID-19 pandemic, different Indonesian provinces had different numbers of COVID-19 infections and fatalities, particularly in West Sumatra Province. This study aimed to investigate the variation of confirmed COVID-19 cases and determine predictors of mortality in hospitalized patients across districts in West Sumatra Province. A retrospective observational study was conducted during the COVID-19 pandemic. From March 2020 to June 2021, 46,005 confirmed cases were collected in the province, of which 42,308 were hospitalized and analyzed. Confirmed cases and deaths were compared by geographic location using spatial analysis. The risk predictors of death were estimated using …

Bayesian Methods In Analyzing The Diagnostic Accuracy\\ For Ordinal Ratings, Yun Yang

Theses and Dissertations

This dissertation focuses on ordinal classification ratings, which are commonly used in medical practice to assess the severity of a disease or condition. For example, a group of radiologists rate a set of mammograms and assign BI-RADS (Breast Imaging Reporting Data System) score for each mammogram. A Bayesian probit hierarchical model is first proposed to analyze this type of data. It links the ordinal ratings with both rater diagnostic skills and patient latent disease severity. Each rater diagnostic skills are quantified with two parameters, diagnostic bias and diagnostic magnifier. Patient latent disease severity is assumed to follow a different normal …

Statistical Inference Based On Elliptically Symmetric Distributions For Directional Data, Zehao Yu

Theses and Dissertations

Directional data arise in many scientific fields such as meteorology, oceanography, geology, zoology, and biomechanics. Geometrically, directional data lie in a spherical space. Although not in a spherical space, compositional data, such as microbiome data, can be mapped from a simplex to a spherical space via the component-wise square-root transformation. Other examples where compositional data emerge as a subject of interest include compositions of minerals in rocks, compositions of chemical mixtures, investment portfolios, and demographic composition of a population. This dissertation aims to develop inference procedures for analyzing directional data in general initially, with later focus shifted to the transformed …