Physical Sciences and Mathematics Commons^™

Spatio-Temporal Analysis Of Point Patterns, Abdul-Nasah Soale

Electronic Theses and Dissertations

In this thesis, the basic tools of spatial statistics and time series analysis are applied to the case study of the earthquakes in a certain geographical region and time frame. Then some of the existing methods for joint analysis of time and space are described and applied. Finally, additional research questions about the spatial-temporal distribution of the earthquakes are posed and explored using statistical plots and models. The focus in the last section is in the relationship between number of events per year and maximum magnitude and its effect on how clustered the spatial distribution is and the relationship between …

Multilevel Models For Longitudinal Data, Aastha Khatiwada

Electronic Theses and Dissertations

Longitudinal data arise when individuals are measured several times during an ob- servation period and thus the data for each individual are not independent. There are several ways of analyzing longitudinal data when different treatments are com- pared. Multilevel models are used to analyze data that are clustered in some way. In this work, multilevel models are used to analyze longitudinal data from a case study. Results from other more commonly used methods are compared to multilevel models. Also, comparison in output between two software, SAS and R, is done. Finally a method consisting of fitting individual models for each …

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

Predicting Intraday Financial Market Dynamics Using Takens' Vectors; Incorporating Causality Testing And Machine Learning Techniques, Abubakar-Sadiq Bouda Abdulai

Electronic Theses and Dissertations

Traditional approaches to predicting financial market dynamics tend to be linear and stationary, whereas financial time series data is increasingly nonlinear and non-stationary. Lately, advances in dynamical systems theory have enabled the extraction of complex dynamics from time series data. These developments include theory of time delay embedding and phase space reconstruction of dynamical systems from a scalar time series. In this thesis, a time delay embedding approach for predicting intraday stock or stock index movement is developed. The approach combines methods of nonlinear time series analysis with those of causality testing, theory of dynamical systems and machine learning (artificial …

Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker

Electronic Theses and Dissertations

Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …

Assessing The Social And Ecological Factors That Influence Childhood Overweight And Obesity, Katie Callahan

Electronic Theses and Dissertations

The prevalence of childhood overweight and obesity is increasing at an alarming rate in the United States. Currently more than 1 in 3 children aged 2-19 are overweight or obese. This is of major concern because childhood overweight and obesity leads to chronic conditions such as type II diabetes and tracks into adulthood, where more severe adverse health outcomes arise. In this study I used the premise of the social ecological model (SEM) to analyze the common levels that a child is exposed to daily; the intrapersonal level, the interpersonal level, the school level, and the community level to better …

Analyses Of 2002-2013 China’S Stock Market Using The Shared Frailty Model, Chao Tang

Electronic Theses and Dissertations

This thesis adopts a survival model to analyze China’s stock market. The data used are the capitalization-weighted stock market index (CSI 300) and the 300 stocks for creating the index. We define the recurrent events using the daily return of the selected stocks and the index. A shared frailty model which incorporates the random effects is then used for analyses since the survival times of individual stocks are correlated. Maximization of penalized likelihood is presented to estimate the parameters in the model. The covariates are selected using the Akaike information criterion (AIC) and the variance inflation factor (VIF) to avoid …

Time Series Decomposition Using Singular Spectrum Analysis, Cheng Deng

Electronic Theses and Dissertations

Singular Spectrum Analysis (SSA) is a method for decomposing and forecasting time series that recently has had major developments but it is not yet routinely included in introductory time series courses. An international conference on the topic was held in Beijing in 2012. The basic SSA method decomposes a time series into trend, seasonal component and noise. However there are other more advanced extensions and applications of the method such as change-point detection or the treatment of multivariate time series. The purpose of this work is to understand the basic SSA method through its application to the monthly average sea …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Comparison Of Different Methods For Estimating Log-Normal Means, Qi Tang

Electronic Theses and Dissertations

The log-normal distribution is a popular model in many areas, especially in biostatistics and survival analysis where the data tend to be right skewed. In our research, a total of ten different estimators of log-normal means are compared theoretically. Simulations are done using different values of parameters and sample size. As a result of comparison, ``A degree of freedom adjusted" maximum likelihood estimator and Bayesian estimator under quadratic loss are the best when using the mean square error (MSE) as a criterion. The ten estimators are applied to a real dataset, an environmental study from Naval Construction Battalion Center (NCBC), …

Some New Probability Distributions Based On Random Extrema And Permutation Patterns, Jie Hao

Electronic Theses and Dissertations

In this paper, we study a new family of random variables, that arise as the distribution of extrema of a random number N of independent and identically distributed random variables X₁,X₂, ..., X_N, where each X_i has a common continuous distribution with support on [0,1]. The general scheme is first outlined, and SUG and CSUG models are introduced in detail where X_i is distributed as U[0,1]. Some features of the proposed distributions can be studied via its mean, variance, moments and moment-generating function. Moreover, we make some other choices for …

Level Crossing Times In Mathematical Finance, Ofosuhene Osei

Electronic Theses and Dissertations

Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .

A Methodology For The Analysis Of Fly Activity Data., Ruoying Wang

Undergraduate Honors Theses

Experiments to learn about the effect of light, sex, and diet on the activity of flies generate great quantities of data that is necessary to analyze. Since different researches and students participate in the analysis of those experiments, it is convenient to have a methodology to analyze the experimental data using software so that the data can be analyzed in a uniform way. Being a double major in mathematics and biology, I am interested in:

• Deciding which statistical procedure to use to analyze the data so that the research questions of the researchers in biology are answered.
• To recommend how …

Modeling Antibiotic Resistance When Adding A New Antibiotic To A Hospital Setting., Brandi N. Canter

Undergraduate Honors Theses

As of now, not many pharmaceutical companies are producing new categories of antibiotics to fight bacterial infections. Therefore, bacteria are building up a resistance to the medications commonly used. Often, antibiotic resistance begins within a hospital. To combat resistance, researchers completed several studies using cycling of the medications that are already in place, but they found either no improvement or the resistance increased with this type of setting. In addition, although preventative infection control measures have been shown to decrease antibiotic resistance for some antibiotics, the level of antibiotic resistance found in hospitals is still extremely high. This motivates the …

Comparison Of Time Series And Functional Data Analysis For The Study Of Seasonality., Jake Allen

Electronic Theses and Dissertations

Classical time series analysis has well known methods for the study of seasonality. A more recent method of functional data analysis has proposed phase-plane plots for the representation of each year of a time series. However, the study of seasonality within functional data analysis has not been explored extensively. Time series analysis is first introduced, followed by phase-plane plot analysis, and then compared by looking at the insight that both methods offer particularly with respect to the seasonal behavior of a variable. Also, the possible combination of both approaches is explored, specifically with the analysis of the phase-plane plots. The …

Solving The Differential Equation For The Probit Function Using A Variant Of The Carleman Embedding Technique., Kelechukwu Iroajanma Alu

Electronic Theses and Dissertations

The probit function is the inverse of the cumulative distribution function associated with the standard normal distribution. It is of great utility in statistical modelling. The Carleman embedding technique has been shown to be effective in solving first order and, less efficiently, second order nonlinear differential equations. In this thesis, we show that solutions to the second order nonlinear differential equation for the probit function can be approximated efficiently using a variant of the Carleman embedding technique.

Power Analysis For Alternative Tests For The Equality Of Means., Haiyin Li

Electronic Theses and Dissertations

The two sample t-test is the test usually taught in introductory statistics courses to test for the equality of means of two populations. However, the t-test is not the only test available to compare the means of two populations. The randomization test is being incorporated into some introductory courses. There is also the bootstrap test. It is also not uncommon to decide the equality of the means based on confidence intervals for the means of these two populations. Are all those methods equally powerful? Can the idea of non-overlapping t confidence intervals be extended to bootstrap confidence intervals? The powers …

A Singular Perturbation Approach To The Fitzhugh-Nagumo Pde For Modeling Cardiac Action Potentials., Jeremy Brooks

Undergraduate Honors Theses

The study of cardiac action potentials has many medical applications. Dr. Dennis Noble first used mathematical models to study cardiac action potentials in the 1960s. We begin our study of cardiac action potentials with one form of the Fitzhugh-Nagumo partial differential equation. We use the non-classical method to produce a closed form solution for the decoupled Fitzhugh Nagumo equation. Using voltage recording data of action potentials in a cardiac myocyte and in purkinje fibers, we estimate parameter values for the closed form solution with standard linear and non-linear regression methods. Results are limited, thus leading us to perturb the solution …

Early Stopping Of A Neural Network Via The Receiver Operating Curve., Daoping Yu

Electronic Theses and Dissertations

This thesis presents the area under the ROC (Receiver Operating Characteristics) curve, or abbreviated AUC, as an alternate measure for evaluating the predictive performance of ANNs (Artificial Neural Networks) classifiers. Conventionally, neural networks are trained to have total error converge to zero which may give rise to over-fitting problems. To ensure that they do not over fit the training data and then fail to generalize well in new data, it appears effective to stop training as early as possible once getting AUC sufficiently large via integrating ROC/AUC analysis into the training process. In order to reduce learning costs involving the …

A Comparative Study Between The Standards Of Learning And In-Class Grades., Randetta Lynn Fuller

Electronic Theses and Dissertations

We examined the Standards of Learning mathematics scores and in-class grades for a rural Virginia county public school system. We looked at third, fourth, fifth, sixth, and seventh grades as well as Algebra I, Algebra II, and Geometry classes. The purpose of this was to determine whether or not there is a strong correlation between the Standards of Learning and the students' in-class grades. Had a strong enough correlation between the Standards of Learning and in-class grades been found we would have used only the in-class grades to predict the Standard of Learning test scores. However, we found that the …

Spousal Concordance In Academic Achievements And Intelligence And Family-Based Association Studies Identified Novel Loci Associated With Intelligence., Yue Pan

Electronic Theses and Dissertations

Assortative Mating, the tendency for mate selection to occur on the basis of similar traits, plays an essential role in understanding the genetic variation on academic achievements and intelligence (IQ). It is an important mechanism explaining spousal concordance. We used principal component analysis (PCA) for spousal correlation. There is a significant positive correlation between spouses by the new variable PC1 (correlation coefficient=0.515, p<0.0001). We further research the genetic factor that affects IQ by using the same data. We performed a low density genome-wide association (GWA) analysis with a family-based association test to identify genetic variants that associated with intelligence as measured by WAIS full-score IQ (FSIQ). NTM at 11q25 (rs411280, p=0.000764) and NR3C2 at 4q31.23 (rs3846329, p=0.000675) were 2 novel genes that haven't been associated with IQ from other studies. This study may serve as a resource for replication in other populations and a foundation for future investigations.

Modeling The Progression Of Discrete Paired Longitudinal Data., Jonathan Wesley Hicks

Electronic Theses and Dissertations

It is our intention to derive a methodology for which to model discrete paired longitudinal data. Through the use of transition matrices and maximum likelihood estimation techniques by means of software, we develop a way to model the progression of such data. We provide an example by applying this method to the Wisconsin Epidemiological Study of Diabetic Retinopathy data set. The data set is comprised of individuals, all diabetics, who have had their eyes examined for diabetic retinopathy. The eyes are treated as paired data, and we have the results of the examination at the four unequally spaced time points …

Interval Estimation For The Ratio Of Percentiles From Two Independent Populations., Pius Matheka Muindi

Electronic Theses and Dissertations

Percentiles are used everyday in descriptive statistics and data analysis. In real life, many quantities are normally distributed and normal percentiles are often used to describe those quantities. In life sciences, distributions like exponential, uniform, Weibull and many others are used to model rates, claims, pensions etc. The need to compare two or more independent populations can arise in data analysis. The ratio of percentiles is just one of the many ways of comparing populations. This thesis constructs a large sample confidence interval for the ratio of percentiles whose underlying distributions are known. A simulation study is conducted to evaluate …

Estimating The Difference Of Percentiles From Two Independent Populations., Romual Eloge Tchouta

Electronic Theses and Dissertations

We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.

Methods For The Analysis Of Developmental Respiration Patterns., Justin Tyler Peyton

Electronic Theses and Dissertations

This thesis looks at the problem of developmental respiration in Sarcophaga crassipalpis Macquart from the biological and instrumental points of view and adapts mathematical and statistical tools in order to analyze the data gathered. The biological motivation and current state of research is given as well as instrumental considerations and problems in the measurement of carbon dioxide production. A wide set of mathematical and statistical tools are used to analyze the time series produced in the laboratory. The objective is to assemble a methodology for the production and analysis of data that can be used in further developmental respiration research.

New Technique For Imputing Missing Item Responses For An Ordinal Variable: Using Tennessee Youth Risk Behavior Survey As An Example., Andaleeb Abrar Ahmed

Electronic Theses and Dissertations

Surveys ordinarily ask questions in an ordinal scale and often result in missing data. We suggest a regression based technique for imputing missing ordinal data. Multilevel cumulative logit model was used with an assumption that observed responses of certain key variables can serve as covariate in predicting missing item responses of an ordinal variable. Individual predicted probabilities at each response level were obtained. Average individual predicted probabilities for each response level were used to randomly impute the missing responses using a uniform distribution. Finally, likelihood ratio chi square statistics was used to compare the imputed and observed distributions. Two other …

Probability And Statistics For Third Through Fifth Grade Classrooms., Melissa Taylor Mckinnon

Electronic Theses and Dissertations

This document contains a variety of lesson plans that can be readily used by a teacher of intermediate students. This thesis contains two units in Probability and one unit in Statistics. Any educator can supplement this document with any curriculum to teach lessons from vocabulary to concept.

Examining Significant Differences Of Gunshot Residue Patterns Using Same Make And Model Of Firearms In Forensic Distance Determination Tests., Heather Lewey

Electronic Theses and Dissertations

In many cases of crimes involving a firearm, police investigators need to know how far the firearm was held from the victim when it was discharged. Knowing this distance, vital questions regarding the re-construction of the crime scene can be known. Often, the original firearm used in commission of a suspected crime is not available for testing or is damaged. Crime laboratories require the original firearm in order to conduct distance determination tests. However, no empirical research has ever been conducted to determine if same make and model firearms produce different results in distance determination testing. It was the purpose …

Self-Management Of Type 2 Diabetes In Appalachina Women., Melissa Joy Magness

Electronic Theses and Dissertations

Gender, minority, and regional-related disparities have been documented in diabetes management. Self-efficacy, the belief in one's ability to carry out the actions mandated by a task, has been identified as a key predictor in glycemic control; however, it has not been investigated in rural, female populations. This cross-sectional, correlation investigation examined the relationships among self-efficacy, depression, and diabetes self-care management in women living in Appalachia with type 2 diabetes. Using Bandura's Social Cognitive Theory, 85 women ages ≥ 21 with type 2 diabetes for a minimum of 6 months who were residents in Appalachia completed the 1) Diabetes Self-Efficacy Scale, …

Beverage Consumption And Hypertension: Findings From The Third National Health And Nutrition Examination Survey., Vishal Arunbhai Mandge

Electronic Theses and Dissertations

The study sample was comprised of 18,953 subjects aged 18 years and older who participated in the Third National Health and Nutrition Examination Survey. Preference for diet soda over regular soda was higher in females as compared to males and in Caucasians as compared to other races. Mean alcohol consumption was almost three times higher in males than in females. Undiagnosed hypertension was more common in males than in females, in 65-90 than in 50-64 year olds, and in people with less than high school education compared to those with higher education. Diastolic pressure was correlated with the level of …