Physical Sciences and Mathematics Commons^™

Static And Dynamic State Estimation Applications In Power Systems Protection And Control Engineering, Ibukunoluwa Olayemi Korede

Doctoral Dissertations

The developed methodologies are proposed to serve as support for control centers and fault analysis engineers. These approaches provide a dependable and effective means of pinpointing and resolving faults, which ultimately enhances power grid reliability. The algorithm uses the Least Absolute Value (LAV) method to estimate the augmented states of the PCB, enabling supervisory monitoring of the system. In addition, the application of statistical analysis based on projection statistics of the system Jacobian as a virtual sensor to detect faults on transmission lines. This approach is particularly valuable for detecting anomalies in transmission line data, such as bad data or …

Generative Adversarial Game With Tailored Quantum Feature Maps For Enhanced Classification, Anais Sandra Nguemto Guiawa

Doctoral Dissertations

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms.

This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A …

Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako

Doctoral Dissertations

This dissertation is in the field of Nonparametric Derivative Estimation using
Penalized Splines. It is conducted in two parts. In the first part, we study the L2
convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …

Multidimensional Investigation Of Tennessee’S Urban Forest, Jillian L. Gorrell

Doctoral Dissertations

Preserving existing trees in urban areas and properly cultivating urban forest conservation and management opportunities is valuable to the ever-growing urban environment and necessary for creating optimal experiences and educational tools to meet the needs of increasing urban populations. This dissertation contains studies investigating several facets of the urban forest, including environmental effects of deforestation and urbanization, tree equity, and urban forest facility management and accessibility. Community education and outreach at arboreta about the importance of the tree canopy can help promote environmental stewardship. A digital questionnaire was electronically distributed to representatives of arboreta certified through the Tennessee Division of …

Large Deviations For Self Intersection Local Times Of Ornstein-Uhlenbeck Processes, Apostolos Gournaris

Doctoral Dissertations

In the area of large deviations, people concern about the asymptotic computation of small probabilities on an exponential scale. The general form of large deviations can be roughly described as: P{Yn ∈ A} ≈ exp{−bnI(A)} (n → ∞), for a random sequence {Yn}, a positive sequence bn with bn → ∞, and a coefficient I(A) ≥ 0. In applications, we often concern about the probability that the random variables take large values, that is we concern about the P{Yn ≥ λ}, where λ > 0. Here, we consider the Ornstein-Uhlenbeck process, study the properties of the local times and self intersection …

Inverse Probability Weighting In Survival Analysis And Network Analysis, Yukun Lu

Doctoral Dissertations

Inverse probability weighting is a popular technique to accommodate selection bias due to non-random sampling and missing data. In the first chapter, we develop an inverse probability weighted estimator and an augmented inverse probability weighted estimator of regression coefficients for a linear model with randomly censored covariates, when the censoring mechanism may be dependent on the outcome. We investigate the asymptotic properties of both estimators and evaluate their finite sample performance through extensive simulation studies. We apply the proposed methods to an Alzheimer’s disease study. In the second chapter, we present an application of network analysis in a study of …

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 …

Estimation Of Causal Effects In Complex Clustered Data, Joshua R. Nugent

Doctoral Dissertations

Analysis of clustered data from randomized trials or observational data often poses theoretical and practical statistical challenges, including but not limited to small numbers of independent units, many adjustment variables, continuous exposures, and/or differential clustering across trial arms. Further, commonly-used parametric methods rely on assumptions that may be violated in practice. Motivated by three scientific questions in public health, methods are developed and/or demonstrated for non-parametric estimation of causal effects. In Chapter 1, methods are elaborated for a cluster randomized trial (CRT) with missing individual-level data at baseline and follow-up, a complex sampling strategy, and limited number of clusters. Chapter …

Applications Of Statistical Physics To Ecology: Ising Models And Two-Cycle Coupled Oscillators, Vahini Reddy Nareddy

Doctoral Dissertations

Many ecological systems exhibit noisy period-2 oscillations and, when they are spatially extended, they undergo phase transition from synchrony to incoherence in the Ising universality class. Period-2 cycles have two possible phases of oscillations and can be represented as two states in the bistable systems. Understanding the dynamics of ecological systems by representing their oscillations as bistable states and developing dynamical models using the tools from statistical physics to predict their future states is the focus of this thesis. As the ecological oscillators with two-cycle behavior undergo phase transitions in the Ising universality class, many features of synchrony and equilibrium …

Bayesian Hierarchical Temporal Modeling And Targeted Learning With Application To Reproductive Health, Herbert P. Susmann

Doctoral Dissertations

The international community via the United Nations Sustainable Development Goals has set the target of universal access to reproductive health-care services, including family planning, by 2030. Progress towards reaching this goal is assessed by tracking appropriate demographic and health indicators at national and subnational levels. This task is challenging, however, in populations where relevant data are limited or of low quality. Statistical models are then needed to estimate and project demographic and health indicators in populations based on the available data. Our first contribution, in Chapter 1, is to unify many existing demographic and health indicator models by proposing an …

Statistical Methods To Study Transposon Sequencing Data: Nonparametric Bayesian Models With Sampling Algorithms, Shai He

Doctoral Dissertations

As the development of Next Generation Sequencing(NGS) technology, researchers can easily obtain data from millions of cells( bulk samples) or just collecting data from a single cell. However, while bulk samples can capture broad changes, it may risk providing an average measurement that is not representative of the genetic state of any individual cell. While single-cell experiments can capture the genetic state of the individual cell, a single cell sample can increase uncertainty, sampling enough cells to gain a representative sample of population is expensive. Therefore, there is a need to integrate information from both bulk and single-cell data to …

Better Understanding Genomic Architecture With The Use Of Applied Statistics And Explainable Artificial Intelligence, Jonathon C. Romero

Doctoral Dissertations

With the continuous improvements in biological data collection, new techniques are needed to better understand the complex relationships in genomic and other biological data sets. Explainable Artificial Intelligence (X-AI) techniques like Iterative Random Forest (iRF) excel at finding interactions within data, such as genomic epistasis. Here, the introduction of new methods to mine for these complex interactions is shown in a variety of scenarios. The application of iRF as a method for Genomic Wide Epistasis Studies shows that the method is robust in finding interacting sets of features in synthetic data, without requiring the exponentially increasing computation time of many …

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 …

Sparse Model Selection Using Information Complexity, Yaojin Sun

Doctoral Dissertations

This dissertation studies and uses the application of information complexity to statistical model selection through three different projects. Specifically, we design statistical models that incorporate sparsity features to make the models more explanatory and computationally efficient.

In the first project, we propose a Sparse Bridge Regression model for variable selection when the number of variables is much greater than the number of observations if model misspecification occurs. The model is demonstrated to have excellent explanatory power in high-dimensional data analysis through numerical simulations and real-world data analysis.

The second project proposes a novel hybrid modeling method that utilizes a mixture …

Gaussian Graphical Models For Omics Data: New Methodology And Applications, Katherine H. Shutta

Doctoral Dissertations

Gaussian graphical models (GGMs) are useful network estimation tools for modeling direct dependencies that characterize multivariate data. The GGM modeling framework is one way to elucidate complex systems-level properties that can be difficult to detect in univariate analyses. In this dissertation, we begin by presenting a tutorial and review of the current state of the field of GGM theory and application. Next, we present a motivating application of GGMs in a study of metabolomic networks associated with chronic distress in women in the Women's Health Initiative (WHI) and in the Nurses' Health Study cohorts. In the third chapter, we present …

Impact Of Loss To Follow-Up And Time Parameterization In Multiple-Period Cluster Randomized Trials And Assessing The Association Between Institution Affiliation And Journal Publication, Jonathan Moyer

Doctoral Dissertations

Difference-in-difference cluster randomized trials (CRTs) use baseline and post-test measurements. Standard power equations for these trials assume no loss to follow-up. We present a general equation for calculating treatment effect variance in difference-in-difference CRTs, with special cases assuming loss to follow-up with replacement of lost participants and loss to follow-up with no replacement but retaining the baseline measurements of all participants. Multiple-period CRTs can represent time as continuous using random coefficients (RC) or categorical using repeated measures ANOVA (RM-ANOVA) analytic models. Previous work recommends the use of RC over RM-ANOVA for CRTs with more than two periods because RC exhibited …

Methods To Improve Inference From Dependent Network Data, Dongah Kim

Doctoral Dissertations

Over the past decade, network research has increased dramatically. Network data are used in many fields because they contain not only covariates of each observation, but also `relationships' between observations. Therefore, statistical analysis of network data has been rapidly developed. However, network data presents many challenges, such as collecting network data, inferring the prevalence of an outcome of interest, and valid statistical testing typically with highly dependent data. The methods discussed in this thesis are developed to improve statistical inference from dependent network data.

High-Dimensional Feature Selection And Multi-Level Causal Mediation Analysis With Applications To Human Aging And Cluster-Based Intervention Studies, Hachem Saddiki

Doctoral Dissertations

Many questions in public health and medicine are fundamentally causal in that our objective is to learn the effect of some exposure, randomized or not, on an outcome of interest. As a result, causal inference frameworks and methodologies have gained interest as a promising tool to reliably answer scientific questions. However, the tasks of identifying and efficiently estimating causal effects from observed data still pose significant challenges under complex data generating scenarios. We focus on (1) high-dimensional settings where the number of variables is orders of magnitude higher than the number of observations; and (2) multi-level settings, where study participants …

Monitoring Mammals At Multiple Scales: Case Studies From Carnivore Communities, Kadambari Devarajan

Doctoral Dissertations

Carnivores are distributed widely and threatened by habitat loss, poaching, climate change, and disease. They are considered integral to ecosystem function through their direct and indirect interactions with species at different trophic levels. Given the importance of carnivores, it is of high conservation priority to understand the processes driving carnivore assemblages in different systems. It is thus essential to determine the abiotic and biotic drivers of carnivore community composition at different spatial scales and address the following questions: (i) What factors influence carnivore community composition and diversity? (ii) How do the factors influencing carnivore communities vary across spatial and temporal …

Measurement Invariance Across Immigrant And Non-Immigrant Populations On Pisa Cognitive And Non-Cognitive Scales, Maritza Casas

Doctoral Dissertations

International large-scale educational assessments (ILSAs) have played a relevant role in educational policies targeting immigrant students across countries as their results are used by governments as input for decision-making purposes. Given the potential impact that ILSAs can have, the psychometric features of these assessments must be carefully assessed and empirical evidence about the extent to which the inferences made based on test results are valid must be collected. To do so, the first step is to determine if the test results have the same meaning across countries and groups of examinees that is, if the measures are invariant so that …

Using Generalizability And Rasch Measurement Theory To Ensure Rigorous Measurement In An International Development Education Evaluation, Louise Bahry

Doctoral Dissertations

Between the United States and Great Britain, over 30 billion USD was spent in 2018 on international aid, over a billion of which is dedicated to education programs alone. Recently, there has been increased attention on the rigorous evaluation of aid-funded programs, moving beyond counting outputs to the measurement of educational impact. The current study uses two methodological approaches (Generalizability (Brennan, 1992, 2001) and Rasch Measurement Theory (Andrich, 1978; Rasch, 1980; Wright & Masters, 1982) to analyze data from math and literacy assessments, and self-report surveys used in an international evaluation of an educational initiative in the Democratic Republic of …

Model-Free Descriptive Modeling For Multivariate Categorical Data With An Ordinal Dependent Variable, Li Wang

Doctoral Dissertations

In the process of statistical modeling, the descriptive modeling plays an essential role in accelerating the formulation of plausible hypotheses in the subsequent explanatory modeling and facilitating the selection of potential variables in the subsequent predictive modeling. Especially, for multivariate categorical data analysis, it is desirable to use the descriptive modeling methods for uncovering and summarizing the potential association structure among multiple categorical variables in a compact manner. However, many classical methods in this case either rely on strong assumptions for parametric models or become infeasible when the data dimension is higher. To this end, we propose a model-free method …

Motor Control-Based Assessment Of Therapy Effects In Individuals Post-Stroke: Implications For Prediction Of Response And Subject-Specific Modifications, Ashley Rice

Doctoral Dissertations

Producing a coordinated motion such as walking is, at its root, the result of healthy communication pathways between the central nervous system and the musculoskeletal system. The central nervous system produces an electrical signal responsible for the excitation of a muscle, and the musculoskeletal system contains the necessary equipment for producing a movement-driving force to achieve a desired motion. Motor control refers to the ability an individual has to produce a desired motion, and the complexity of motor control is a mathematical concept stemming from how the electrical signals from the central nervous system translate to muscle activations. Exercising a …

Geometric Representation Learning, Luke Vilnis

Doctoral Dissertations

Vector embedding models are a cornerstone of modern machine learning methods for knowledge representation and reasoning. These methods aim to turn semantic questions into geometric questions by learning representations of concepts and other domain objects in a lower-dimensional vector space. In that spirit, this work advocates for density- and region-based representation learning. Embedding domain elements as geometric objects beyond a single point enables us to naturally represent breadth and polysemy, make asymmetric comparisons, answer complex queries, and provides a strong inductive bias when labeled data is scarce. We present a model for word representation using Gaussian densities, enabling asymmetric entailment …

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 …