Physical Sciences and Mathematics Commons^™

Advances In Differentially Methylated Region Detection And Cure Survival Models, Daniel Ahmed Alhassan

Doctoral Dissertations

"This dissertation focuses on two areas of statistics: DNA methylation and survival analysis. The first part of the dissertation pertains to the detection of differentially methylated regions in the human genome. The varying distribution of gaps between succeeding genomic locations, which are represented on the microarray used to quantify methylation, makes it challenging to identify regions that have differential methylation. This emphasizes the need to properly account for the correlation in methylation shared by nearby locations within a specific genomic distance. In this work, a normalized kernel-weighted statistic is proposed to obtain an optimal amount of "information" from neighboring locations …

Recurrent Event Data Analysis With Mismeasured Covariates, Ravinath Alahakoon Mudiyanselage

Doctoral Dissertations

"Consider a study with n units wherein every unit is monitored for the occurrence of an event that can recur with random end of monitoring. At each recurrence, p concomitant variables associated to the event recurrence are recorded with q (q ≤ p) collected with errors. Of interest in this dissertation is the estimation of the regression parameters of event time regression models accounting for the covariates. To circumvent the problem of bias and consistency associated with model's parameter estimation in the presence of measurement errors, we propose inference for corrected estimating functions with well-behaved roots under additive measurement errors …

Essays On Conditional Heteroscedastic Time Series Models With Asymmetry, Long Memory, And Structural Changes, K C M R Anjana Bandara Yatawara

Doctoral Dissertations

"The volatility of asset returns is usually time-varying, necessitating the introduction of models with a conditional heteroskedastic variance structure. In this dissertation, several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroskedastic (GARCH) type models, are further generalized to accommodate more dynamic features of asset returns such as asymmetry, long memory, and structural breaks. First, we introduce a hybrid structure that combines short-memory asymmetric Glosten, Jagannathan, and Runkle (GJR) formulation and the long-memory fractionally integrated GARCH (FIGARCH) process for modeling financial volatility. This formulation not only can model volatility clusters and capture asymmetry but also considers the characteristic of long …

Efficient High Order Ensemble For Fluid Flow, John Carter

Doctoral Dissertations

"This thesis proposes efficient ensemble-based algorithms for solving the full and reduced Magnetohydrodynamics (MHD) equations. The proposed ensemble methods require solving only one linear system with multiple right-hand sides for different realizations, reducing computational cost and simulation time. Four algorithms utilize a Generalized Positive Auxiliary Variable (GPAV) approach and are demonstrated to be second-order accurate and unconditionally stable with respect to the system energy through comprehensive stability analyses and error tests. Two algorithms make use of Artificial Compressibility (AC) to update pressure and a solenoidal constraint for the magnetic field. Numerical simulations are provided to illustrate theoretical results and demonstrate …

Meta-Analysis Of Mesenchymal Stem Cell Gene Expression Data From Obese And Non-Obese Patients, Dakota William Shields

Masters Theses

"The prevalence of gene expression microarray datasets in public repositories gives opportunity to analyze biologically interesting datasets without running the laboratory aspect in house. Such experimentation is expensive in terms of finances, time, and expertise, which often results in low numbers of replicates. Meta-analysis techniques attempt to overcome issues due to few biological or technical replicates by combining separate experiments together to increase statistical power. Proper statistical considerations help to offset issues like simultaneous testing of thousands of genes, unintended hybridization, and other noises.

Microarrays contain light intensities from tens of thousands of hybridized probes giving a measure of gene …

Survivor Bond Models For Securitizing Longevity Risk, Priscilla Mansah Codjoe

Doctoral Dissertations

"Longevity risk is the risk that a reference population’s mortality rates deviate from what is projected from prior life tables. This is due to discoveries in biological sciences, improved public health measures, and nutrition, which have dramatically increased life expectancy. Longevity risk raises life insurers’ liability, increasing product costs and reserves. Securitization through longevity derivatives is a way of dealing with this risk.

To enhance the pricing of life contingent products, we present an additive type mortality model in the style of the Lee-Carter. This model incorporates policyholder covariates. By using counting processes and martingale machinery, we obtain close form …

Semiparametric Estimation With Clustered Right Censored Data Via Multivariate Gaussian Random Fields, Fathima Zahra Sainul Abdeen

Doctoral Dissertations

Consider a fixed number of clustered areas identified by their geographical coordinate that are monitored for the occurrences of an event such as pandemic, epidemic, migration to name a few. Data collected on units at all areas include time varying covariates and other environmental factors that may affect event occurrences. The event times in every area can be independent. They can also be correlated with correlation between two units induced by an unobservable frailty. In both cases, the collected data is considered pairwise to account for spatial correlation between all pair of areas. The pairwise right censored data is probit-transformed …

Continuous And Discrete Models For Optimal Harvesting In Fisheries, Nagham Abbas Al Qubbanchee

Masters Theses

"This work focuses on the logistic growth model, where the Gordon-Schaefer model is considered in continuous time. We view the Gordon-Schaefer model as a bioeconomic equation involved in the fishing business, considering biological rates, carrying capacity, and total marginal costs and revenues. In [25], the authors illustrate the analytical solution of the Schaefer model using the integration by parts method and two theorems. The theorems have many assumptions with many different strategies. Due to the nature of the problem, the optimal control system involves many equations and functions, such as the second root of the equation. We concentrate on Theorem …

Modeling Time Series With Conditional Heteroscedastic Structure, Ratnayake Mudiyanselage Isuru Panduka Ratnayake

Doctoral Dissertations

"Models with a conditional heteroscedastic variance structure play a vital role in many applications, including modeling financial volatility. In this dissertation several existing formulations, motivated by the Generalized Autoregressive Conditional Heteroscedastic model, are further generalized to provide more effective modeling of price range data well as count data. First, the Conditional Autoregressive Range (CARR) model is generalized by introducing a composite range-based multiplicative component formulation named the Composite CARR model. This formulation enables a more effective modeling of the long and short-term volatility components present in price range data. It treats the long-term volatility as a stochastic component that in …

Prediction Intervals For Fractionally Integrated Time Series And Volatility Models, Rukman Ekanayake

Doctoral Dissertations

"The two of the main formulations for modeling long range dependence in volatilities associated with financial time series are fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) and hyperbolic generalized autoregressive conditional heteroscedastic (HYGARCH) models. The traditional methods of constructing prediction intervals for volatility models, either employ a Gaussian error assumption or are based on asymptotic theory. However, many empirical studies show that the distribution of errors exhibit leptokurtic behavior. Therefore, the traditional prediction intervals developed for conditional volatility models yield poor coverage. An alternative is to employ residual bootstrap-based prediction intervals. One goal of this dissertation research is to develop …

Integrating Snp Data And Imputation Methods Into The Dna Methylation Analysis Framework, Yuqing Su

Doctoral Dissertations

"DNA methylation is a widely studied epigenetic modification that can influence the expression and regulation of functional genes, especially those related to aging, cancer and other diseases. The common goal of methylation studies is to find differences in methylation levels between samples collected under different conditions. Differences can be detected at the site level, but regulated methylation targets are most commonly clustered into short regions. Thus, identifying differentially methylated regions (DMRs) between different groups is of prime interest. Despite advanced technology that enables measuring methylation genome-wide, misinterpretations in the readings can arise due to the existence of single nucleotide polymorphisms …

Count Data Time Series Models And Their Applications, Yi Zhang

Doctoral Dissertations

“Due to fast developments of advanced sensors, count data sets have become ubiquitous in many fields. Modeling and forecasting such time series have generated great interest. Modeling can shed light on the behavior of the count series and to see how they are related to other factors such as the environmental conditions under which the data are generated. In this research, three approaches to modeling such count data are proposed.

First, a periodic autoregressive conditional Poisson (PACP) model is proposed as a natural generalization of the autoregressive conditional Poisson (ACP) model. By allowing for cyclical variations in the parameters of …

Quantifying Effects Of Sleep Deprivation On Cognitive Performance, Quang Nghia Le

Masters Theses

“The most commonly used metric for evaluating alertness and vigilance is the Psychomotor Vigilance Test (PVT), previous studies have indicated that alertness and vigilance can be affected by the lack of sleep as a function of sleep loss. This study explores methods to predict median psychomotor vigilance reaction times. The data used in this study comes from a series of tests and surveys conducted on volunteer students. The data set contains many potential predictors of PVT and one aspect of the study was to identify variables that are useful in prediction. The performances of various prediction methods that allow for …

Fuzzy Logistic Regression For Detecting Differential Dna Methylation Regions, Tarek M. Bubaker Bennaser

Doctoral Dissertations

“Epigenetics is the study of changes in gene activity or function that are not related to a change in the DNA sequence. DNA methylation is one of the main types of epigenetic modifications, that occur when a methyl chemical group attaches to a cytosine on the DNA sequence. Although the sequence does not change, the addition of a methyl group can change the way genes are expressed and produce different phenotypes. DNA methylation is involved in many biological processes and has important implications in the fields of biomedicine and agriculture.

Statistical methods have been developed to compare DNA methylation at …

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 …

Reliability Analysis For Systems With Outsourced Components, Zhengwei Hu

Doctoral Dissertations

"The current business model for many industrial firms is to function as system integrators, depending on numerous outsourced components from outside component suppliers. This practice has resulted in tremendous cost savings; it makes system reliability analysis, however, more challenging due to the limited component information available to system designers. The component information is often proprietary to component suppliers. Motivated by the need of system reliability prediction with outsourced components, this work aims to explore feasible ways to accurately predict the system reliability during the system design stage. Four methods are proposed. The first method reconstructs component reliability functions using limited …

The Correlation Between Sleep And Lifespan In Drosophila Melanogaster, Joshua Randall Lisse

Masters Theses

”Adequate sleep is associated with an individual’s health. Too little sleep is associated with many health problems, including cardiovascular disease, obesity, and a general increase in all-cause mortality. Yet the molecular changes that link poor sleep and changes in health are still not well understood. Individuals have a unique daily need for sleep, and deviations from the animal’s regular sleeping patterns can be indicative of, or result in, underlying changes in its health. Therefore, we hypothesize that changes in the sleep architecture in Drosophila melanogaster reflect changes in the fly’s health.

We determined sleep architecture in wild-type male flies over …

Novel Statistical Modeling Of Sleep Patterns In Drosophila Melanogaster, Luyang Wang

Doctoral Dissertations

”Sleep is one of the most important behaviors in animals, yet many aspects of sleep are not well understood. In humans, sleep has been shown to impact different aspects of health and cognitive performance. The fruit fly, Drosophila melanogaster, can be used as a model organism to investigate sleep patterns over an entire lifespan. The sleep-wake status can be recorded every minute over the life of individual flies, resulting in a wealth of data for identifying meaningful aspects of sleep. In this work, a framework based on statistical modeling methods is developed for sleep data collected on fruit flies …

Less Is More: Beating The Market With Recurrent Reinforcement Learning, Louis Kurt Bernhard Steinmeister

Masters Theses

"Multiple recurrent reinforcement learners were implemented to make trading decisions based on real and freely available macro-economic data. The learning algorithm and different reinforcement functions (the Differential Sharpe Ratio, Differential Downside Deviation Ratio and Returns) were revised and the performances were compared while transaction costs were taken into account. (This is important for practical implementations even though many publications ignore this consideration.) It was assumed that the traders make long-short decisions in the S&P500 with complementary 3-month treasury bill investments. Leveraged positions in the S&P500 were disallowed. Notably, the Differential Sharpe Ratio and the Differential Downside Deviation Ratio are risk …

New Developments Of Dimension Reduction, Lei Huo

Doctoral Dissertations

"Variable selection becomes more crucial than before, since high dimensional data are frequently seen in many research areas. Many model-based variable selection methods have been developed. However, the performance might be poor when the model is mis-specified. Sufficient dimension reduction (SDR, Li 1991; Cook 1998) provides a general framework for model-free variable selection methods.

In this thesis, we first propose a novel model-free variable selection method to deal with multi-population data by incorporating the grouping information. Theoretical properties of our proposed method are also presented. Simulation studies show that our new method significantly improves the selection performance compared with those …

On Modeling Quantities For Insurer Solvency Against Catastrophe Under Some Markovian Assumptions, Daniel Jefferson Geiger

Doctoral Dissertations

"Insurance companies sometimes face catastrophic losses, yet they must remain solvent enough to meet the legal obligation of covering all claims. Catastrophes can result in large damages to the policyholders, causing the arrival of numerous claims to insurance companies at once. Furthermore, the severity of an event could impact the time until the next occurrence. An insurer needs certain levels of startup capital to meet all claims, and then must have adequate reserves on a continual basis, even more so when catastrophes occur. This work examines two facets of these matters: for an infinite time horizon, we extend and develop …

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 …

Development Of A Variogram Approach To Spatial Outlier Detection Using A Supplemental Digital Elevation Model Dataset, Zane Daniel Helwig

Masters Theses

"When developing a ground water model, the quality of the dataset should first be evaluated. Spatial outliers can lead to predictions which are not representative of actual conditions. In order to isolate misrepresentative points, a method is presented which examines the experimental variogram of a ground water elevation dataset. To define a threshold variance between pairs of ground water elevation measures, ground elevation values from a digital elevation model (DEM) are used to determine a maximum reasonable variance expected to occur on the experimental variogram. To determine appropriate DEM parameters, a separate study was also done which observed characteristic behavior …

Comparing Region Level Testing Methods For Differential Dna Methylation Analysis, Arnold Albert Harder

Masters Theses

”Finding possible connections and solutions to help fight progression of diseases is a major area of research. Genomics is a primary path of research in disease research. Through the DNA sequence, possible connections to diseases have been found. However, most methods for fixing issues within a DNA sequence are still out of reach. One potential path is to investigate epigenetic modifications, such as DNA methylation. DNA methylation occurs when a methyl group attached to cytosines on the DNA sequence. Statistical methods can be used to identify sites or regions of significant differences in methylation levels between groups ( e. g. …

Family-Based Association Studies Of Autism In Boys Via Facial-Feature Clusters, Luke Andrew Settles

Masters Theses

"Autism spectrum disorder (ASD) refers to a set of developmental disorders with varied attributes. Due to its substantial heterogeneity in terms of behavioral and clinical phenotypes, it is challenging to discern the genetic biomarkers behind ASD, even though the disease is known to be genetic in nature. This serves as a motivation to detect relationships between single nucleotide polymorphisms (SNPs) and a causal autism disease susceptibility locus (DSL) within more homogeneous subgroups. Recently, clinically meaningful subclassifications of ASD have been discovered utilizing facial features of prepubescent boys. Therefore, through the employment of data from 44 prepubertal Caucasian boys with ASD …

A Functional Data Analytic Approach For Region Level Differential Dna Methylation Detection, Mohamed Salem F. Milad

Doctoral Dissertations

"DNA methylation is an epigenetic modification that can alter gene expression without a DNA sequence change. The role of DNA methylation in biological processes and human health is important to understand, with many studies identifying associations between specific methylation patterns and diseases such as cancer. In mammals, DNA methylation almost always occurs when a methyl group attaches to a cytosine followed by a guanine (i.e. CpG dinucleotides) on the DNA sequence. Many statistical methods have been developed to test for a difference in DNA methylation levels between groups (e.g. healthy vs disease) at individual cytosines. Site level testing is often …

Local Holomorphic Extension Of Cauchy Riemann Functions, Brijitta Antony

Doctoral Dissertations

"The purpose of this dissertation is to give an analytic disc approach to the CR extension problem. Analytic discs give a very convenient tool for holomorphic extension of CR functions. The type function is introduced and showed how these type functions have direct application to important questions about CR extension. In this dissertation the CR extension theorem is proved for a rigid hypersurface M in C² given by y = (Re ω)^m(Im ω)ⁿ where m and n are non-negative integers. If the type function is identically zero at the origin, then there is no CR extension. …

On The Double Chain Ladder For Reserve Estimation With Bootstrap Applications, Larissa Schoepf

Masters Theses

"To avoid insolvency, insurance companies must have enough reserves to fulfill their present and future commitment-refer to in this thesis as outstanding claims towards policyholders. This entails having an accurate and reliable estimate of funds necessary to cover those claims as they are presented. One of the major techniques used by practitioners and researchers is the single chain ladder method. However, though most popular and widely used, the method does not offer a good understanding of the distributional properties of the way claims evolve. In a series of recent papers, researchers have focused on two potential components of outstanding claims, …

Modeling Daily Electricity Load Curve Using Cubic Splines And Functional Principal Components, Abdelmonaem Salem Jornaz

Doctoral Dissertations

"Forecasting electricity load is very important to the electric utilities as well as producers of power because accurate predictions can cut down costs by avoiding power shortages or surpluses. Of specific interest is the 24-hour daily electricity load profile, which provides insight into periods of high demand and periods where the use of electricity is at a minimum. Researchers have proposed many approaches to modeling electricity prices, real-time load, and day-ahead demand, with varying success. In this dissertation three new approaches to modeling and forecasting the 24-hour daily electricity load profiles are presented. The application of the proposed methods is …

Steam Flooding Screening And Eor Prediction By Using Clustering Algorithm And Data Visualization, Na Zhang

Masters Theses

"Enhanced Oil Recovery (EOR) techniques are vitally important in the oil industry because these techniques could not only extend the life of wells, but also produce 10% to 30% additional oil from the reservoir. However, selecting the most suitable EOR techniques for unknown reservoirs is not easy for decision making. Based on literature, EOR screening criteria could help to find the best candidates for unknown projects, which is classified into two categories: conventional EOR screening and advanced EOR screening. In this research, an artificial intelligent (AI) method, hierarchical clustering algorithm, is adapted to analyze both steam flooding projects and worldwide …