Statistics and Probability Commons^™

Multiple Imputation Using Influential Exponential Tilting In Case Of Non-Ignorable Missing Data, Kavita Gohil

College of Graduate Studies: Theses & Dissertations

Modern research strategies rely predominantly on three steps, data collection, data analysis, and inference. In research, if the data is not collected as designed, researchers may face challenges of having incomplete data, especially when it is non-ignorable. These situations affect the subsequent steps of evaluation and make them difficult to perform. Inference with incomplete data is a challenging task in data analysis and clinical trials when missing data related to the condition under the study. Moreover, results obtained from incomplete data are prone to biases. Parameter estimation with non-ignorable missing data is even more challenging to handle and extract useful …

Public Perception Of Different Planting Techniques Using Augmented Reality, Sultana Quader Tania

College of Graduate Studies: Theses & Dissertations

The objective of this study was to measure public perception of the different planting techniques (block and matrix), which are used at visitor information centers (VICs) and other rights of way (ROW) areas. The main factors that affect public perception of planting techniques were identified through an extensive literature review and qualitative survey from four welcome centers in the state of Georgia. The ranking of those indicators, based on public preferences, was discovered through a quantitative survey. During the first phase of the quantitative survey, images of block and matrix were used. An iOS-based user-friendly and cost-effective augmented reality (AR) …

Nonparametric Misclassification Simulation And Extrapolation Method And Its Application, Congjian Liu

College of Graduate Studies: Theses & Dissertations

The misclassification simulation extrapolation (MC-SIMEX) method proposed by Küchenho et al. is a general method of handling categorical data with measurement error. It consists of two steps, the simulation and extrapolation steps. In the simulation step, it simulates observations with varying degrees of measurement error. Then parameter estimators for varying degrees of measurement error are obtained based on these observations. In the extrapolation step, it uses a parametric extrapolation function to obtain the parameter estimators for data with no measurement error. However, as shown in many studies, the parameter estimators are still biased as a result of the parametric extrapolation …

Generalization Of Kullback-Leibler Divergence For Multi-Stage Diseases: Application To Diagnostic Test Accuracy And Optimal Cut-Points Selection Criterion, Chen Mo

College of Graduate Studies: Theses & Dissertations

The Kullback-Leibler divergence (KL), which captures the disparity between two distributions, has been considered as a measure for determining the diagnostic performance of an ordinal diagnostic test. This study applies KL and further generalizes it to comprehensively measure the diagnostic accuracy test for multi-stage (K > 2) diseases, named generalized total Kullback-Leibler divergence (GTKL). Also, GTKL is proposed as an optimal cut-points selection criterion for discriminating subjects among different disease stages. Moreover, the study investigates a variety of applications of GTKL on measuring the rule-in/out potentials in the single-stage and multi-stage levels. Intensive simulation studies are conducted to compare the performance …

Artificial Neural Network Models For Pattern Discovery From Ecg Time Series, Mehakpreet Kaur

College of Graduate Studies: Theses & Dissertations

Artificial Neural Network (ANN) models have recently become de facto models for deep learning with a wide range of applications spanning from scientific fields such as computer vision, physics, biology, medicine to social life (suggesting preferred movies, shopping lists, etc.). Due to advancements in computer technology and the increased practice of Artificial Intelligence (AI) in medicine and biological research, ANNs have been extensively applied not only to provide quick information about diseases, but also to make diagnostics accurate and cost-effective. We propose an ANN-based model to analyze a patient's electrocardiogram (ECG) data and produce accurate diagnostics regarding possible heart diseases …

Introduction To Game Theory: A Discovery Approach, Jennifer Firkins Nordstrom

Linfield Authors Book Gallery

Game theory is an excellent topic for a non-majors quantitative course as it develops mathematical models to understand human behavior in social, political, and economic settings. The variety of applications can appeal to a broad range of students. Additionally, students can learn mathematics through playing games, something many choose to do in their spare time! This text also includes an exploration of the ideas of game theory through the rich context of popular culture. It contains sections on applications of the concepts to popular culture. It suggests films, television shows, and novels with themes from game theory. The questions in …

Bayesian Kinetic Modeling For Tracer-Based Metabolomic Data, Xu Zhang

Theses and Dissertations--Statistics

Kinetic modeling of the time dependence of metabolite concentrations including the unstable isotope labeled species is an important approach to simulate metabolic pathway dynamics. It is also essential for quantitative metabolic flux analysis using tracer data. However, as the metabolic networks are complex including extensive compartmentation and interconnections, the parameter estimation for enzymes that catalyze individual reactions needed for kinetic modeling is challenging. As the pa- rameter space is large and multi-dimensional while kinetic data are comparatively sparse, the estimation procedure (especially the point estimation methods) often en- counters multiple local maximum such that standard maximum likelihood methods may yield …

Statistical Intervals For Various Distributions Based On Different Inference Methods, Yixuan Zou

Theses and Dissertations--Statistics

Statistical intervals (e.g., confidence, prediction, or tolerance) are widely used to quantify uncertainty, but complex settings can create challenges to obtain such intervals that possess the desired properties. My thesis will address diverse data settings and approaches that are shown empirically to have good performance. We first introduce a focused treatment on using a single-layer bootstrap calibration to improve the coverage probabilities of two-sided parametric tolerance intervals for non-normal distributions. We then turn to zero-inflated data, which are commonly found in, among other areas, pharmaceutical and quality control applications. However, the inference problem often becomes difficult in the presence of …

Moment Kernels For T-Central Subspace, Weihang Ren

Theses and Dissertations--Statistics

The T-central subspace allows one to perform sufficient dimension reduction for any statistical functional of interest. We propose a general estimator using a third moment kernel to estimate the T-central subspace. In particular, in this dissertation we develop sufficient dimension reduction methods for the central mean subspace via the regression mean function and central subspace via Fourier transform, central quantile subspace via quantile estimator and central expectile subsapce via expectile estima- tor. Theoretical results are established and simulation studies show the advantages of our proposed methods.

Measuring Change: Prediction Of Early Onset Sepsis, Aric Schadler

Theses and Dissertations--Statistics

Sepsis occurs in a patient when an infection enters into the blood stream and spreads throughout the body causing a cascading response from the immune system. Sepsis is one of the leading causes of morbidity and mortality in today’s hospitals. This is despite published and accepted guidelines for timely and appropriate interventions for septic patients. The largest barrier to applying these interventions is the early identification of septic patients. Early identification and treatment leads to better outcomes, shorter lengths of stay, and financial savings for healthcare institutions. In order to increase the lead time in recognizing patients trending towards septicemia …

Simultaneous Tolerance Intervals For Response Surface And Mixture Designs Using The Adjusted Product Set Method, Aisaku Nakamura

Theses and Dissertations--Statistics

Various methods for constructing simultaneous tolerance intervals for regression models have been developed over the years, but all of them can be shown to be conservative. In this thesis, extensive simulations are conducted to evaluate the degree of conservatism with respect to their coverage probabilities. A new strategy to fit simultaneous tolerance intervals on linear models is proposed by modifying an existing method, which we call the adjusted product set (APS) method. The APS method will also be used to construct simultaneous tolerance bands on response surface and mixture designs.

The Application Of Machine Learning Models In The Concussion Diagnosis Process, Sujit Subhash

Masters Theses

“Concussions represent a growing health concern and are challenging to diagnose and manage. Roughly four million concussions are diagnosed every year in the United States. Although research into the application of advanced metrics such as neuroimages and blood biomarkers has shown promise, they are yet to be implemented at a clinical level due to cost and reliability concerns. Therefore, concussion diagnosis is still reliant on clinical evaluations of symptoms, balance, and neurocognitive status and function. The lack of a universal threshold on these assessments makes the diagnosis process entirely reliant on a physician’s interpretation of these assessment scores. This study …

Lifestyle Factors And Social Determinants As Predictors Of Weight/Body Mass Index, Uthman Alhaji Baba

Walden Dissertations and Doctoral Studies

Obesity is a major public health concern that includes the risk of developing cardiovascular disease and premature death in adults. Previous studies have established the relationship between gender, educational level, household income and respondents’ weight but additional research is needed to factor the nature of education in relation to gender differences, diet, and other important behavioral mediators such as social determinants. The purpose of this quantitative cross-sectional study is to determine the extent to which frequency of physical activity, household income, social determinants of health (money for balanced meals, finances at the end of month, and poor mental health), respondent …

Noise, Avian Abundance, And Productivity At Banding Stations Across The Continental United States, Amber M.B. Ng, Michael L. Pontius, Stacy L. Deruiter, Darren S. Proppe

University Faculty Publications and Creative Works

Noise is an increasingly common component of the natural world, due in large part to human activity. Anthropogenic noise negatively impacts abundance, health, and reproduction in many songbird populations. A few studies have reported altered abundance at larger scales. But whether continental trends are being detected at banding stations, which also offer data on productivity and survivorship, is unknown. Further, it is not known whether localized trends correlate with population trends observed at larger scales. We used breeding season data from 1160 constant-effort banding stations (Monitoring Avian Productivity and Survivorship; MAPS) and a spatially explicit noise model to determine whether …

Enhancing Models And Measurements Of Traffic-Related Air Pollutants For Health Studies Using Dispersion Modeling And Bayesian Data Fusion, Stuart A. Batterman, Veronica J. Berrocal, Chad Milando, Owais Gilani, Saravanan Arunachalam, K. Max Zhang

Faculty Journal Articles

Research Report 202 describes a study led by Dr. Stuart Batterman at the University of Michigan, Ann Arbor and colleagues. The investigators evaluated the ability to predict traffic-related air pollution using a variety of methods and models, including a line source air pollution dispersion model and sophisticated spatiotemporal Bayesian data fusion methods. Exposure assessment for traffic-related air pollution is challenging because the pollutants are a complex mixture and vary greatly over space and time. Because extensive direct monitoring is difficult and expensive, a number of modeling approaches have been developed, but each model has its own limitations and errors.

Dr. …

Neutroalgebra Is A Generalization Of Partial Algebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we recall, improve, and extend several definitions, properties and applications of our previous 2019 research referred to NeutroAlgebras and AntiAlgebras (also called NeutroAlgebraic Structures and respectively AntiAlgebraic Structures). Let be an item (concept, attribute, idea, proposition, theory, etc.). Through the process of neutrosphication, we split the nonempty space we work on into three regions {two opposite ones corresponding to and , and one corresponding to neutral (indeterminate) (also denoted ) between the opposites}, which may or may not be disjoint – depending on the application, but they are exhaustive (their union equals the whole space). A NeutroAlgebra …

Predicting Student Success In Arcadia University’S Math Courses, Chutong Wu, Tong Zhu, Yijin Qiu

Capstone Showcase

This project examines the relative efficacy of Arcadia’s math placement test and math SAT scores in predicting student success, and explores whether SAT scores alone might suffice for certain courses.

An Introduction To Copulas, Yifan Guo, Geng Zhang

Capstone Showcase

Copulas are the mathematical functions that connect the distribution functions of univariate random variables to form multivariate distributions. We define copulas, present some of their key properties, and provide examples of their applications.

Genetic Algorithm Guidance Of A Constraint Programming Solver For The Multiple Traveling Salesman Problem, Jessica M. Rudd, Andrew M. Henshaw, Lauren Staples, Sanjoosh Akkineni, Lin Li, Joe Demaio

Published and Grey Literature from PhD Candidates

This project developed a metaheuristic approach to the Multiple Traveling Salesman Problem that pairs a custom genetic algorithm with a conventional combinatorial optimization solver. This combined approach was used to build an optimal route for two popular radio show hosts to visit each of the 37 Atlanta area Jersey Mike's Subs in one day. This supported a fundraising eort to send children with chronic and terminal illnesses to Disney World through an organization called Bert's Big Adventure. Atlanta-area Jersey Mike's locations donated 100% of proceeds earned on this Day of Giving to Bert's Big Adventure. With the suggested route developed …

Lévy Processes: Characterizing Volcanic And Financial Time Series, Peter Kwadwo Asante

Open Access Theses & Dissertations

In this work, we use the Diffusion Entropy Analysis (DEA) to analyze and detect the scaling properties of time series from both emerging and well established markets as well as volcanic eruptions recorded by a seismic station, both financial and volcanic time series data are known to have high frequencies (i.e they are collected at an extremely fine scale). The objective is to determine the characterization i.e whether they follow a Gaussian or Lévy distribution. If they do follow a Lévy distribution we are then interested in finding if they are characterized by a Lévy walk which has a finite …

Predicting Stochastic Volatility For Extreme Fluctuations In High Frequency Time Series, Md Al Masum Bhuiyan

Open Access Theses & Dissertations

This work is devoted to the study of modeling high frequency time series including extreme fluctuations. As the high frequency data are collected at extremely fine scales, the fluctuations can capture the dynamics of data that evolve over time. A class of volatility models with time-varying parameters is used to forecast the volatility in a stationary condition at different lags. The modeling of stationary time series with consistent properties facilitates prediction with much certainty.

A large set of high frequency financial returns, closing prices of stock markets, high magnitudes of seismograms generated by the natural earthquakes, and the mining explosions …

Applications Of Ornstein-Uhlenbeck Type Stochastic Differential Equations, Osei Kofi Tweneboah

Open Access Theses & Dissertations

In this Dissertation, we show with plausible arguments that the Stochastic Differential Equations (SDEs) arising on the superposition and coupling system of independent Ornstein-Uhlenbeck process is a new method available in modern literature that takes the properties and behavior of the data into consideration when performing the statistical analysis of the time series.

The time series to be analyzed is thought of as a source of fluctuations, and thus we need a model that takes this behavior into consideration when performing such analysis. Most of the standard methods fail to take into account the physical behavior of the time series, …

Robust Estimation And Inference For Multivariate Financial Data, Afua Kwakyewaa Amoako Dadey

Open Access Theses & Dissertations

Predicting and forecasting are routine day-to-day activities that guide us in making the best possible choices. They play an integral role in financial analysis. A lot of work has been done on one dimensional geometric Brownian motion (GBM) in stock price prediction. In this line of work, we focus mainly on how to use the one dimensional geometric Brownian motion and the multidimensional geometric Brownian motion in predicting future stock prices. There are several stock prices in the financial market and the multidimensional geometric Brownian motion gives a more realistic prediction compared to the one dimensional GBM. The reason being …

General Penalized Logistic Regression For Gene Selection In High-Dimensional Microarray Data Classification, Derrick Kwesi Bonney

Open Access Theses & Dissertations

High-dimensional data has become a major research area in the field of genetics, bioinformatics and bio-statistics due to advancement of technologies. Some common issues of modeling high-dimensional gene expression data are that many of the genes may not be relevant. Also, reducing the dimensions of the data using penalized logistic regression is one of the major challenges when there exists a high correlation among genes. High-dimension data correspond to the situation where the number of variables is greater or larger than the number of observations. Gene selection proved to be an effective way to improve the results of many classification …

Stochastic Modeling Of Earthquakes And Option Pricing Using Bns-Gamma-Ou Model, Mandela Bright Quashie

Open Access Theses & Dissertations

High frequency data are becoming increasingly popular these days. They are fundamental in basically every facet of people’s lives. They are the determining factors in hedging in the field of finance. In geology, they help in the accurate prediction of earthquakes’ magnitude which goes along way to help save lives and properties.

High frequency data are also used more and more frequently for speculations. For this reason, it is important not only for scientists to apply models allowing correct quantification of these data, but also to improve the eciency of these models.

The Black-Scholes model, which is widely used because …

Technological Software In Mathematics, Courtney Kish

Williams Honors College, Honors Research Projects

Technology has been advancing significantly over the years. One area that has been affected is mathematics. Technological software has been developed that has allowed for mathematics to be done using software programs. For example, WebAssign allows students to complete online math homework and example practice problems, as well as watch videos to explain topics in math. However, like all things, this is not without downfalls. While this technology offers students access to online lectures and instant feedback, cheating and costly expenses also come with it.

In this research paper, I will discuss the benefits and shortcomings of different technological software …

Home Sales As A Time Series Model, Noah R. Hellenthal

Williams Honors College, Honors Research Projects

Rational Expectations Hypothesis is an economic theorem that states that our best way to predict the future is by looking at the past. While this theory is typically used to address inflation, the same concept can be used when predicting future home sales. With the failure of subprime mortgages and the burst of the housing market bubble in 2008, home sales are proven to be an appropriate indication of how the U.S. economy is performing. Through time series analysis, I will be able to construct a model with monthly home sales data from the U.S. Census Bureau. Due to seasonality …

Spatially Adaptive Estimation Of Spectrum, Yi None Xie

Open Access Theses & Dissertations

When analyzing a stationary time series, one of the questions we are often interested in is how to estimate its spectrum. Many approaches have been proposed to this end. Most are focused on smoothing the periodogram using a single smoothing parameter across all Fourier frequencies. In this paper, we smooth the log periodogram by placing a spatially adaptive prior called the dynamic shrinkage prior, so that varying degrees of smoothing may be applied to different intervals of Fourier frequencies, resulting in less biased estimates of the spectrum. Further research will extend this approach to spectral estimation for nonstationary time series.

An Examination Of Covid-19 Statistical Modeling, Shane Vaughan

Williams Honors College, Honors Research Projects

The 2019 novel coronavirus, also known as COVID-19, is an infectious disease which was first reported in late 2019 and soon spread to become a global pandemic, prompting major action from world governments. Soon after, many institutions began attempts to analyze and predict the spread and severity of the disease via statistical modeling. Some information is not available for public consumption; however, a number of institutions have published the results of their analyses and some have made public repositories of the code used to build the models. This research paper attempts use these and other resources to examine the modeling …

Ai And Machine Learning Usage In Actuarial Science, Joanna Riley

Williams Honors College, Honors Research Projects

Some people in the world work hard and do whatever it takes in order to get a job that they love. There are others that don’t care about their jobs and solely perform them in order to make money. So, there are individuals or groups that wouldn’t care if a machine or computer were to replace them in their job, but others would be devastated. The question for this paper is: Can actuaries be completely replaced by computers, or do we need the human mind in order to make proper decisions and judgements?

Key words and phrases: actuarial science, artificial …