Statistics and Probability Commons^™

Classification Of High-Dimensional Data Based On Multiple Testing Methods, Chong Ma

Theses and Dissertations

Supervised and unsupervised classification are common topics in machine learning in both scientific and industrial fields, which usually involve three tasks: prediction, exploration, and explanation. False discovery rate (FDR) theory has a close connection to classical classification theory, which must be employed in a sophisticated way to achieve good performance in various contexts. The study aims to explore novel supervised classifiers and unsupervised classification approaches for functional data and high-dimensional data in genome study by using FDR, respectively. One work develops a novel classifier for functional data by casting the classification problem into a multiple testing task, which involves using …

Examining The Confirmatory Tetrad Analysis (Cta) As A Solution Of The Inadequacy Of Traditional Structural Equation Modeling (Sem) Fit Indices, Hangcheng Liu

Theses and Dissertations

Structural Equation Modeling (SEM) is a framework of statistical methods that allows us to represent complex relationships between variables. SEM is widely used in economics, genetics and the behavioral sciences (e.g. psychology, psychobiology, sociology and medicine). Model complexity is defined as a model’s ability to fit different data patterns and it plays an important role in model selection when applying SEM. As in linear regression, the number of free model parameters is typically used in traditional SEM model fit indices as a measure of the model complexity. However, only using number of free model parameters to indicate SEM model complexity …

Estimating The Respiratory Lung Motion Model Using Tensor Decomposition On Displacement Vector Field, Kingston Kang

Theses and Dissertations

Modern big data often emerge as tensors. Standard statistical methods are inadequate to deal with datasets of large volume, high dimensionality, and complex structure. Therefore, it is important to develop algorithms such as low-rank tensor decomposition for data compression, dimensionality reduction, and approximation.

With the advancement in technology, high-dimensional images are becoming ubiquitous in the medical field. In lung radiation therapy, the respiratory motion of the lung introduces variabilities during treatment as the tumor inside the lung is moving, which brings challenges to the precise delivery of radiation to the tumor. Several approaches to quantifying this uncertainty propose using a …

Development Of Lower Rio Grande River Water Quality Transportation Numerical Model For Bi-National River Management, Jose O. Gonzalez

Theses and Dissertations

Traditionally, water quality modelling has focused on modelling individual water bodies. However, water quality management problems must be analyzed at the larger scale to include influences from various water bodies that are interconnected. This paper provides a study on the hydrologic and quality transportation calculation by developing a hydrodynamic (unsteady state) channel routing model using a water-balanced approach. A one dimension Lagrangian river model was developed and applied to the 210 plus miles for the lower Rio Grande River Basin from the Falcon Dam to the head water of Brownsville that pours onto the Gulf of Mexico. This model can …

Bayesian Flexible Modeling Of Interval-Censored Failure Time Data, Sheng-Yang Wang

Theses and Dissertations

Interval-censored data are a special type of survival data, in which the survival time is not accurately observed but known to fall within a specific time interval. Interval censored data commonly arise in real-life epidemiological and medical studies that involve periodic examinations. In this dissertation, several semi-parametric regression models are investigated to provide flexible modeling and robust inference for interval censored data from Bayesian perspectives.

Chapter 1 provides a detailed description about interval-censored data and gives several examples. Existing models and methods for analyzing such interval-censored data are reviewed as well. Chapter 2 develops a unified Bayesian estimation approach under …

Topics In Group Testing With Multiple Infections, Peijie Hou

Theses and Dissertations

Group testing, dating back to the early 1940s, was first proposed to screen for syphilis among US inductees during World War II (Dorfman, 1943). Since then, the benefits of reducing testing costs by employing group testing have been demonstrated in many areas, such as drug discovery, genetics, and infectious disease testing. Traditionally, statistical research in group testing has largely been motivated by applications involving a single infection. With the recent development of multiplex assays that can diagnose multiple infections simultaneously, generalizing the existing group testing literature to incorporate multiple infections is a natural and necessary next step. This dissertation consists …

Semiparametric Estimation And Inference In Causal Inference And Measurement Error Models, Jianxuan Liu

Theses and Dissertations

This dissertation research has focused on theoretical and practical developments of semiparametric modeling and statistical inference for high dimensional data and measurement error data. In causal inference framework, when evaluating the effectiveness of medical treatments or social intervention policies, the average treatment effect becomes fundamentally important. We focus on propensity score modelling in treatment effect problems and develop new robust tools to overcome the curse of dimensionality. Furthermore, estimating and testing the effect of covariates of interest while accommodating many other covariates is an important problem in many scientific practices, including but not limited to empirical economics, public health and …

Improved Simultaneous Estimation Of Location And System Reliability Via Shrinkage Ideas, Beidi Qiang

Theses and Dissertations

In decision theory, when several parameters need to be estimated simultaneously, many standard estimators can be improved, in terms of a combined loss function. The problem of finding such estimators has been well studied in the literature, but mostly under parametric settings, which is inappropriate for heavy-tailed distributions. In the first part of this dissertation, a robust simultaneous estimator of location is proposed using the shrinkage idea. A nonparametric Bayesian estimator is also discussed as an alternative. The proposed estimators do not assume a specific parametric distribution and they do not require the existence of finite moments. The performance of …

Parametric, Nonparametric And Semiparametric Approaches In Profile Monitoring Of Poisson Data, Sepehr Piri

Theses and Dissertations

Profile monitoring is a relatively new approach in quality control best used when the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles under the assumption of the correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or, at least uncertain. Consequently, we consider monitoring Poisson profiles via three methods, a nonparametric (NP) method using penalized splines, a nonparametric (NP) method using wavelets and a semi parametric (SP) procedure that combines both parametric …

Tuning Optimization Software Parameters For Mixed Integer Programming Problems, Toni P. Sorrell

Theses and Dissertations

The tuning of optimization software is of key interest to researchers solving mixed integer programming (MIP) problems. The efficiency of the optimization software can be greatly impacted by the solver’s parameter settings and the structure of the MIP. A designed experiment approach is used to fit a statistical model that would suggest settings of the parameters that provided the largest reduction in the primal integral metric. Tuning exemplars of six and 59 factors (parameters) of optimization software, experimentation takes place on three classes of MIPs: survivable fixed telecommunication network design, a formulation of the support vector machine with the ramp …

The Generalized Monotone Incremental Forward Stagewise Method For Modeling Longitudinal, Clustered, And Overdispersed Count Data: Application Predicting Nuclear Bud And Micronuclei Frequencies, Rebecca Lehman

Theses and Dissertations

With the influx of high-dimensional data there is an immediate need for statistical methods that are able to handle situations when the number of predictors greatly exceeds the number of samples. One such area of growth is in examining how environmental exposures to toxins impact the body long term. The cytokinesis-block micronucleus assay can measure the genotoxic effect of exposure as a count outcome. To investigate potential biomarkers, high-throughput assays that assess gene expression and methylation have been developed. It is of interest to identify biomarkers or molecular features that are associated with elevated micronuclei (MN) or nuclear bud (Nbud) …

Longitudinal And Geographical Modeling Of Circular Data With An Application To Sudden Infant Death Syndrome, Xinyan Cai

Theses and Dissertations

The aim of this thesis is to study seasonality of death in U.S. infants who died from SIDS. We also propose to investigate secular trends and geographical patterns of seasonal patterns of mortality. The application of circular statistics is used to describe the seasonality of the month of death in infants who died from SIDS in 1990, 2000 and 2010. The secular trends of seasonal patterns of SIDS mortality are investigated using a circular linear regression model after adjusting for potential confounders. The geographical variation in seasonal patterns of SIDS mortality is explored from the U.S. map and quantified by …

Statistical Methods For Multivariate And Correlated Data, Xinling Xu

Theses and Dissertations

A commonly encountered data type in real life is count data, especially in selfreported behavioral studies. One issue of the self-reported count data is the inaccuracy. In the first part of the dissertation, we are going to address one specific type of inaccuracy in bivariate count data–heaping. Copula functions are used for the formulation of the bivariate distribution. Using copula functions for solving data inaccuracy problems is still a new area, which we are going to explore in this dissertation.

We also discuss the methods for variable selection when the explanatory variables are highly correlated. In particular, our method is …

Evaluation Of Goodness-Of-Fit Tests For The Cox Proportional Hazards Model With Time-Varying Covariates, Shanshan Hong

Theses and Dissertations

The proportional hazards (PH) model, proposed by Cox (1972), is one of the most popular survival models for analyzing time-to-event data. To use the PH model properly, one must examine whether the data satisfy the PH assumption. An alternative model should be suggested if the PH assumption is invalid. The main purpose of this thesis is to examine the performance of five existing methods for assessing the PH assumption. Through extensive simulations, the powers of five different existing methods are compared; these methods include the likelihood ratio test, the Schoenfeld residuals test, the scaled Schoenfeld residuals test, Lin et al. …

Functional Data Smoothing Methods And Their Applications, Songqiao Huang

Theses and Dissertations

In many subjects such as psychology, geography, physiology or behavioral science, researchers collect and analyze non-traditional data, i.e., data that do not consist of a set of scalar or vector observations, but rather a set of sequential observations measured over a fine grid on a continuous domain, such as time, space, etc. Because the underlying functional structure of the individual datum is of interest, Ramsay and Dalzell (1991) named the collection of topics involving analyzing these functional observations functional data analysis (FDA). Topics in functional data analysis include data smoothing, data registration, regression analysis with functional responses, cluster analysis on …

Nonparametric Inference For Orderings And Associations Between Two Random Variables, Chuan-Fa Tang

Theses and Dissertations

Ordering and dependency are two aspects to describe the relationship between two random variables. In this thesis, we choose two hypothesis testing problems to tackle; i.e., a goodness-of-fit test for uniform stochastic ordering and one for positive quadrant dependence. For the test for uniform stochastic ordering, we propose new nonparametric tests based on ordinal dominance curves. We derive the limiting distributions of test statistics and provide the least favorable configuration to determine critical values. Numerical evidence is presented to support our theoretical results, and we apply our methods to a real data set. An extension for random right-censored data is …

Marginal Structural Cox Model For Survival Data With Treatment-Confounder Feedback, Yanan Zhang

Theses and Dissertations

In an observational longitudinal study, there can be time-varying exposure/treatment and time-varying confounders. When the confounders affect the exposure and prior exposure also has an impact on levels of confounders, there is treatment confounder feedback. To admit estimation of unbiased causal effects, these conditions need to be hold, exchangeability, positivity, consistency. The traditional method of conditioning on potential confounders does not meet these 3 conditions. Therefore, parameter estimates from traditional Cox model are biased casual effect estimates when the treatment confounder feedback exists. The marginal structural Cox model can be used to address this issue. By calculating and including inverse …

Adversarial Decision Making In Counterterrorism Applications, Dogucan Mazicioglu

Theses and Dissertations

Our main objective is to improve decision making in counterterrorism applications by implementing expected utility for prescriptive decision making and prospect theory for descriptive modeling. The areas that we aim to improve are behavioral modeling of adversaries with multi objectives in counterterrorism applications and incorporating risk attitudes of decision makers to risk matrices in assessing risk within an adversarial counterterrorism framework. Traditionally, counterterrorism applications have been approached on a single attribute basis. We utilize a multi-attribute prospect theory approach to more realistically model the attacker’s behavior, while using expected utility theory to prescribe the appropriate actions to the defender. We …

Comparing The Structural Components Variance Estimator And U-Statistics Variance Estimator When Assessing The Difference Between Correlated Aucs With Finite Samples, Anna L. Bosse

Theses and Dissertations

Introduction: The structural components variance estimator proposed by DeLong et al. (1988) is a popular approach used when comparing two correlated AUCs. However, this variance estimator is biased and could be problematic with small sample sizes.

Methods: A U-statistics based variance estimator approach is presented and compared with the structural components variance estimator through a large-scale simulation study under different finite-sample size configurations.

Results: The U-statistics variance estimator was unbiased for the true variance of the difference between correlated AUCs regardless of the sample size and had lower RMSE than the structural components variance estimator, providing better type 1 error …

Weighted Quantile Sum Regression For Analyzing Correlated Predictors Acting Through A Mediation Pathway On A Biological Outcome, Bhanu M. Evani

Theses and Dissertations

Abstract

Weighted Quantile Sum Regression for Analyzing Correlated Predictors Acting Through a Mediation Pathway on a Biological Outcome

By

Bhanu M. Evani, Ph.D.

A thesis submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at Virginia Commonwealth University.

Virginia Commonwealth University, 2017.

Major Director: Robert A. Perera, Asst. Professor, Department of Biostatistics

This work examines mediated effects of a set of correlated predictors using the recently developed Weighted Quantile Sum (WQS) regression method. Traditionally, mediation analysis has been conducted using the multiple regression method, first proposed by Baron and Kenny (1986), which has since …

Application Of The Fisher Dimer Model To Dna Condensation, John C. Baker Iii

Theses and Dissertations

This paper considers the statistical mechanics occupation of the edge of a single helix of DNA by simple polymers. Using Fisher's exact closed form solution for dimers on a two-dimensional lattice, a one-dimensional lattice is created mathematically that is occupied by dimers, monomers, and holes. The free energy, entropy, average occupation, and total charge on the lattice are found through the usual statistical methods. The results demonstrate the charge inversion required for a DNA helix to undergo DNA condensation.

A Multi-Method Exploration Of The Genetic And Environmental Risks Contributing To Tobacco Use Behaviors In Young Adulthood, Elizabeth K. Do

Theses and Dissertations

Tobacco use remains the leading preventable cause of morbidity and mortality in both the United States and worldwide. Twin and family studies have demonstrated that both genetic and environmental factors are important contributors to tobacco use behaviors. Understanding how genes, the environment, and their interactions is critical to the development of public health interventions that focus on the reduction of tobacco related morbidity and mortality. However, few studies have examined the transition from adolescent to young adulthood – the time when many individuals are experimenting with and developing patterns of tobacco use. This dissertation thesis seeks to provide a comprehensive …

Measurement Invariance And Psychometric Properties Of Career Indecision Profile-65 Scores: College Student And Non-College Samples, Casey J. Zobell

Theses and Dissertations

This thesis reports the results of a study conducted to examine psychometric properties of Career Indecision Profile-65 scores, including measurement invariance between college student and non-college samples. The responses of 529 college students and 472 non-college students to an online survey revealed that a four-factor structure fit the data in both samples well. Metric invariance was not supported. Six-week test-retest reliability was found to be high, and in the expected range. The tendency to maximize was found to be correlated strongly with one of the four factors. This study furthered the psychometric research for the Career Indecision Profile-65 and found …

A Statistical Approach To Characterize And Detect Degradation Within The Barabasi-Albert Network, Mohd-Fairul Mohd-Zaid

Theses and Dissertations

Social Network Analysis (SNA) is widely used by the intelligence community when analyzing the relationships between individuals within groups of interest. Hence, any tools that can be quantitatively shown to help improve the analyses are advantageous for the intelligence community. To date, there have been no methods developed to characterize a real world network as a Barabasi-Albert network which is a type of network with properties contained in many real-world networks. In this research, two newly developed statistical tests using the degree distribution and the L-moments of the degree distribution are proposed with application to classifying networks and detecting degradation …

Development And Application Of Bayesian Semiparametric Models For Dependent Data, Junshu Bao

Theses and Dissertations

Dependent data are very common in many research fields, such as medicine (repeated measures), finance (time series), traffic (clustered), etc. Effective control/modeling of the dependency among data can enhance the performance of the models and result in better prediction. In many cases, the correlation itself may be of great interest. In this dissertation, we develop novel Bayesian semi-/nonparametric regression models to analyze data with various dependence structures. In Chapter 2, a Bayesian non- parametric multivariate ordinal regression model is proposed to fit drinking behavior survey data from DWI offenders. The responses are two-dimensional ordinal data, drinking frequency and drinking quantity …

Novel Methods For Analyzing Longitudinal Data With Measurement Error In The Time Variable, Caroline Munindi Mulatya

Theses and Dissertations

In some longitudinal studies, the observed time points are often confounded with measurement error due to the sampling conditions, resulting into data with measurement error in the time variable. This type of data occurs mainly in observational studies when the onset of a longitudinal process is unknown or in clinical trials when individual visits do not take place as specified by the study protocol, but are often rounded to coincide with the study protocol. Methodological and inferential implications of error in time varying covariates for both linear and nonlinear models have been studied widely. In this dissertation, we shift attention …

Bayesian Nonparametric Approaches To Multiple Testing, Density Estimation, And Supervised Learning, William Cipolli Iii

Theses and Dissertations

This dissertation presents methods for several applications of Polya tree models. These novel nonparametric approaches to the problems of multiple testing, density estimation and supervised learning provide an alternative to other parametric and nonparametric models. In Chapter 2, the proposed approximate finite Polya tree multiple testing procedure is very successful in correctly classifying the observations with non-zero mean in a computationally efficient manner; this holds even when the non-zero means are simulated from a mean-zero distribution. Further, the model is capable of this for “interestingly different” observations in the cases where that is of interest. Chapter 3 proposes discrete, and …

Quantifying Transit Access In New York City: Formulating An Accessibility Index For Analyzing Spatial And Social Patterns Of Public Transportation, Maxwell S. Siegel

Theses and Dissertations

This paper aims to analyze accessibility within New York City’s transportation system through creating unique accessibility indices. Indices are detailed and implemented using GIS, analyzing the distribution of transit need and access. Regression analyses are performed highlighting relationships between demographics and accessibility and recommendations for transit expansion are presented.

Analysis And Modeling Of U.S. Army Recruiting Markets, Joshua L. Mcdonald

Theses and Dissertations

The United States Army Recruiting Command (USAREC) is charged with finding, engaging, and ultimately enlisting young Americans for service as Soldiers in the U.S. Army. USAREC must decide how to allocate monthly enlistment goals, by aptitude and education level, across its 38 subordinate recruiting battalions in order to maximize the number of enlistment contracts produced each year. In our research, we model the production of enlistment contracts as a function of recruiting supply and demand factors which vary over the recruiting battalion areas of responsibility. Using county-level data for the period of recruiting year RY2010 through RY2013 mapped to recruiting …

Clustering Theory And Data Driven Health Care Strategies, Takayuki Iguchi

Theses and Dissertations

DoD health care requires reform with growing costs causing concerns of decreased military capability. One proposed radical strategy to fix current health care delivery systems is to organize medical teams around patients with similar treatment requirements. This is a clustering problem; how do you partition the set of patients so that each group has similar treatment needs? We provide advances in clustering theory relevant to this new health care strategy. In particular, we create fast certifiably optimal k-means clustering using what is known as Probably Certifiably Correct (PCC) algorithms which achieves state-of-the-art performance under certain models. Inspired by the health …