Statistics and Probability Commons^™

A New Generalized Gamma-Weibull Distribution And Its Applications, Nihimat Iyebuhola Aleshinloye, Samuel Adewale Aderoju, Alfred Adewole Abiodun, Bako Lukmon Taiwo

Al-Bahir

In this paper, a New Generalized Gamma-Weibull (NGGW) distribution is developed by compounding Weibull and generalized gamma distribution. Some mathematical properties such as moments, Rényi entropy and order statistics are derived and discussed. The maximum likelihood estimation (MLE) method is used to estimate the model parameters. The proposed model is applied to two real-life datasets to illustrate its performance and flexibility as compared to some other competing distributions. The results obtained show that the new distribution fits each of the data better than the other competing distributions.

Knowledge, Attitude, And Behavioral Intention About Oral Cancer Among Public Health Students In Southeast Georgia, Ravneet Kaur, Gulzar H. Shah

Biostatistics, Epidemiology & Environmental Health Sciences: Faculty Publications

Background: Oral cancer (OC) is a significant public health problem; however, the degree to which the future public health workforce is aware of this issue is not well researched. The purpose of this study is to explore the level of knowledge, attitudes, and behavioral intentions about OC among public health students.
Materials and Methods: A sequential exploratory mixed-method research design was employed for this study. Using quantitative and qualitative measures, a survey was administered to 129 public health students. Subsequently, to understand the quantitative findings, two follow-up focus groups were conducted with survey participants.
Results: We found …

Classification Of Land Cover On Sand Dunes, Heleyna Tucker, Micah Sterk

22nd Annual Celebration of Undergraduate Research and Creative Activity (2023)

As members of the Hope College Coastal Research Group, we have studied the mechanisms for and effects of sand transport. In particular, we have worked to model vegetation coverage in West Michigan sand dune complexes in order to better understand how sand movement and resident vegetation affect one another. We use aerial drone imagery to develop machine learning algorithms for creating ground cover classification mappings in an automated way. Our team collected drone imagery ranging from high-resolution, low-altitude photographs to high-altitude stitched and rectified orthomosaics. We developed accurate ground cover classification methods for the low-altitude imagery and then explored ways …

Here Come The Floods: Classification Of Rain-On-Snow Induced Flooding In Nevada, Emma Watts

Student Research Symposium

Given Nevada’s history of destructive flooding resulting from rain falling on mountainous snowpack, often called rain-on-snow (ROS) events, there is a great need to incorporate these events and their residual effects in infrastructure design methods. Examining relationships between USGS streamflow measurements and climate variables (specifically precipitation, temperature, and snowpack) obtained from neighboring SNOTEL stations provides means by which to classify ROS-induced floods from ROS events. Using both temperature and snowpack-based criterion to classify ROS events, this project differentiates between non-ROS and ROS-induced floods in a subset of USGS stations across the Sierra Nevada and reveals that ROS-induced floods produce, on …

Generating Optimal Space-Filling Designs With Particle Swarm Optimization, Rebekah Scott

Student Research Symposium

In 1935, Ronald Fisher published The Design of Experiments, establishing classical designs for various types of experiments. With the rise of computing power came optimal design, where statisticians can better customize designs according to the needs of the researchers running the experiment. This research focuses on generating optimal MaxMin space-filling designs with particle swarm optimization using various distance metrics (Manhattan, Euclidean, etc). Interestingly, changing the distance metric in the objective function had a minimal effect on the design, except for Aitchison geometry on the simplex. Space-filling designs are optimal for supporting high-order models with only a small sacrifice in prediction …

Introduction To Ensemble Watershed Segmentation, Scout Jarman

Student Research Symposium

Compared to color images, hyperspectral images are high dimensional, containing hundreds of channels of information. To distill this information, and capture spatial information, image segmentation is used to group similar pixels together. A popular image segmentation algorithm is the marker-based Watershed Transform. One difficulty with this algorithm is choosing the markers, or locations, that seed the algorithm. There are various approaches for automatic marker placement depending on the application, with little consensus on the most general method for hyperspectral images. We propose using an ensemble of random segmentations. Specifically, we investigate a simple, unbiased random marker placement strategy to generate …

A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin

Honors College Theses

Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …

Multilevel Optimization With Dropout For Neural Networks, Gary Joseph Saavedra

Mathematics & Statistics ETDs

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full …

A New Approach To Proper Orthogonal Decomposition With Difference Quotients, Sarah Locke Eskew, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

In a Recent Work (Koc Et Al., SIAM J. Numer. Anal. 59(4), 2163–2196, 2021), the Authors Showed that Including Difference Quotients (DQs) is Necessary in Order to Prove Optimal Pointwise in Time Error Bounds for Proper Orthogonal Decomposition (POD) Reduced Order Models of the Heat Equation. in This Work, We Introduce a New Approach to Including DQs in the POD Procedure. Instead of Computing the POD Modes using All of the Snapshot Data and DQs, We Only Use the First Snapshot Along with All of the DQs and Special POD Weights. We Show that This Approach Retains All of the …

Rank-Based Inference For Survey Sampling Data, Akim Adekpedjou, Huybrechts F. Bindele

Mathematics and Statistics Faculty Research & Creative Works

For regression models where data are obtained from sampling surveies, the statistical analysis is often based on approaches that are either non-robust or inefficient. The handling of survey data requires more appropriate techniques, as the classical methods usually result in biased and inefficient estimates of the underlying model parameters. This article is concerned with the development of a new approach of obtaining robust and efficient estimates of regression model parameters when dealing with survey sampling data. Asymptotic properties of such estimators are established under mild regularity conditions. To demonstrate the performance of the proposed method, Monte Carlo simulation experiments are …

State Gross Domestic Product Predictions Using Hierarchical Clustering And Multivariate Time Series, Austin Dae Nietfeld

Mathematics Senior Capstone Papers

This research was conducted to determine the weight certain taxes and expenditures have over state Gross Domestic Product(GDP) as well as how accurately these predictors can predict future GDP. The motivation behind this project comes from a desire to find the most efficient way to increase the GDP of states with poorer economies. This will improve the quality of life of citizens of these states. To come to a consensus as to what predictors are most influential, Hierarchical Clustering will be used to split the states into four groups. The average of each tax, expenditure and GDP from 2015-2020 will …

Regression Analysis Of Injuries On Nfl Quarterbacks, Julie Weems

Mathematics Senior Capstone Papers

Risk assessment is an important aspect of many careers such as first responders and the military. This is no different for people who play sports, especially people who are in contact sports such as football. These players’ lives can be changed forever with one bad hit. The goal of this research is to analyze the probability of an injury for the National Football League’s (NFL) quarterbacks. It is hard to predict when, what, and where an injury will occur, because of this very little work has been done on the subject matter in a general form. The goal of this …

Firefighter Safety, Haynes Mandino

Mathematics Senior Capstone Papers

There are close to 1.2 million career and volunteer firefighters across the United States. In the year 2020 alone 62 of these firefighters died and 64,875 were injured. The following research was performed to determine if the firefighter profession has become safer due to new standards and regulations. Each year the National Fire Protection Agency(NFPA) and the Federal Emergency Management Agency(FEMA) collect data on the number of firefighter deaths and injuries, in order to determine if the standards and regulations are keeping firefighters safe. Statistical hypothesis testing and linear regression were performed on the data to show if in fact …

Does The Three Point Shot Affect Winning Percentage, Marcamus Winn

Mathematics Senior Capstone Papers

The three-point shot, introduced in the late 1970s, is a shot that occurs typically 24 feet away from the basket at the professional level. Strategically the game of basketball was originally based on two-point field goals. Recently, there has been a noticeable trend in the popularity of the three-point shot amongst professional teams. Nowadays, three point shot attempts account for more than a third of average NBA shot selection. Statistical analysis is becoming integral to athletics. Statistics has become a critical component to the development of not only on court basketball strategies, but also team structure as well. There are …

Changing Nfl Playoff Overtime Rules To Create Equal Opportunities To Win A Game, Matthew Silvia

Honors Projects in Mathematics

The NFL has attempted to create fair overtime rules over the course of the past decade; however, this study is interested in determining what playoff overtime rule (or rules) could the NFL implement to result in outcomes where both teams have a relatively equal chance of winning a game. This study aims to find which overtime rules work best at minimizing the differences between teams who possess the ball first versus teams that kick the ball off to start an overtime period. By collecting various NFL statistics from ESPN.com and FantasyOutsiders.com, this study hopes to run multiple simulations of different …

Econ 603: Time Series Analysis, Kenneth M. Rich

GMAS Course Syllabi

No abstract provided.

Math 576: Mathematical Statistics Ii, Hailin Sang

GMAS Course Syllabi

No abstract provided.

Math 776: Robust Statistics, Xin (Sheen) Dang

GMAS Course Syllabi

No abstract provided.

Mktg 666: Mktg 666 Research Methods 2 Seminar, Saim Kashmiri

GMAS Course Syllabi

No abstract provided.

Nhm 526: Statistics I In Nutrition And Hospitality Management, Hyun-Woo (David) Joung Ph.D.

GMAS Course Syllabi

No abstract provided.

Influence Diagnostics For Generalized Estimating Equations Applied To Correlated Categorical Data, Louis Vazquez

Statistical Science Theses and Dissertations

Influence diagnostics in regression analysis allow analysts to identify observations that have a strong influence on model fitted probabilities and parameter estimates. The most common influence diagnostics, such as Cook’s Distance for linear regression, are based on a deletion approach where the results of a model with and without observations of interest are compared. Here, deletion-based influence diagnostics are proposed for generalized estimating equations (GEE) for correlated, or clustered, nominal multinomial responses. The proposed influence diagnostics focus on GEEs with the baseline-category logit link function and a local odds ratio parameterization of the association structure. Formulas for both observation- and …

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 …

A Diffusion Network Event History Estimator, Jeffrey J. Harden, Bruce A. Desmarais, Mark Brockway, Frederick J. Boehmke, Scott J. Lacombe, Fridolin Linder, Hanna Wallach

Government: Faculty Publications

Research on the diffusion of political decisions across jurisdictions typically accounts for units’ influence over each other with (1) observable measures or (2) by inferring latent network ties from past decisions. The former approach assumes that interdependence is static and perfectly captured by the data. The latter mitigates these issues but requires analytical tools that are separate from the main empirical methods for studying diffusion. As a solution, we introduce network event history analysis (NEHA), which incorporates latent network inference into conventional discrete-time event history models. We demonstrate NEHA’s unique methodological and substantive benefits in applications to policy adoption in …

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 …

Modeling The Probability Of A Successful Stolen Base Attempt In Major League Baseball, Cade Stanley

Senior Theses

In Major League Baseball (MLB), the outcome of a stolen base attempt has important implications. Success moves the runner closer to scoring, while failure records an out and removes the runner from the basepaths altogether. Therefore, it is important that the decision by a coach or player to steal a base is well-informed. In this thesis, I explore a statistical approach to making this decision. I train logistic regression and random forest models, using data about the game situation and about the runner, pitcher, and catcher involved in the stolen base attempt, to estimate the probability that a stolen base …

Prevalence Of Sars-Cov-2 Antibodies In Liberty University Student Population, Emily Bonus

Senior Honors Theses

In 2020, the virus SARS-CoV-2 gained attention as it spread around the world. Its antibodies are poorly understood, and little research focuses on those with few COVID-19 complications yet large numbers of close contacts: university students. This longitudinal study recorded SARS-CoV-2 antibody presence in 107 undergraduate Liberty University students twice during early 2021. After extensive data cleaning and the application of various statistical tests and ANOVAs, the data seems to show that in the case of COVID-19 infections, SARS-CoV-2 IgM antibodies are immediately produced, and then IgG antibodies follow later. However, the COVID-19 vaccine causes the production of both IgM …

Community Participation And Perspectives Of Ambondrolava Mangrove Restoration Project, Nadine Shannon

Independent Study Project (ISP) Collection

Madagascar’s mangrove forests are intertidal ecosystems that provide numerous valuable ecosystem services but are nonetheless under pressure from large amounts of deforestation. On the southwestern coast of Madagascar, the village of Ambondrolava practices community led management of the mangrove and its resources. This research project studied the evolution of the mangrove area using GIS data, and investigated, through interviews, the relationship between the local community of Ambondrolava and the organizations that manage the mangrove ecosystem. From 2000 to 2018, the zone of the mangrove has experienced a net loss in area every year, despite reforestation efforts. Most community members interviewed …

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, …