Statistics and Probability Commons^™

Multi-State Models For Interval Censored Data With Competing Risk, Shaoceng Wei

Theses and Dissertations--Statistics

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk.

Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model …

Empirical Likelihood Confidence Band, Shihong Zhu

Theses and Dissertations--Statistics

The confidence band represents an important measure of uncertainty associated with a functional estimator and empirical likelihood method has been proved to be a viable approach to constructing confidence bands in many cases. Using the empirical likelihood ratio principle, this dissertation developed simultaneous confidence bands for many functions of fundamental importance in survival analysis, including the survival function, the difference and ratio of survival functions, the hazards ratio function, and other parameters involving residual lifetimes. Covariate adjustment was incorporated under the proportional hazards assumption. The proposed method can be very useful when, for example, an individualized survival function is desired …

New Results In Ell_1 Penalized Regression, Edward A. Roualdes

Theses and Dissertations--Statistics

Here we consider penalized regression methods, and extend on the results surrounding the l1 norm penalty. We address a more recent development that generalizes previous methods by penalizing a linear transformation of the coefficients of interest instead of penalizing just the coefficients themselves. We introduce an approximate algorithm to fit this generalization and a fully Bayesian hierarchical model that is a direct analogue of the frequentist version. A number of benefits are derived from the Bayesian persepective; most notably choice of the tuning parameter and natural means to estimate the variation of estimates – a notoriously difficult task for the …

Developments In Nonparametric Regression Methods With Application To Raman Spectroscopy Analysis, Jing Guo

Theses and Dissertations--Epidemiology and Biostatistics

Raman spectroscopy has been successfully employed in the classification of breast pathologies involving basis spectra for chemical constituents of breast tissue and resulted in high sensitivity (94%) and specificity (96%) (Haka et al, 2005). Motivated by recent developments in nonparametric regression, in this work, we adapt stacking, boosting, and dynamic ensemble learning into a nonparametric regression framework with application to Raman spectroscopy analysis for breast cancer diagnosis. In Chapter 2, we apply compound estimation (Charnigo and Srinivasan, 2011) in Raman spectra analysis to classify normal, benign, and malignant breast tissue. We explore both the spectra profiles and their derivatives to …

Nonlinear Hierarchical Models For Longitudinal Experimental Infection Studies, Michael David Singleton

Theses and Dissertations--Epidemiology and Biostatistics

Experimental infection (EI) studies, involving the intentional inoculation of animal or human subjects with an infectious agent under controlled conditions, have a long history in infectious disease research. Longitudinal infection response data often arise in EI studies designed to demonstrate vaccine efficacy, explore disease etiology, pathogenesis and transmission, or understand the host immune response to infection. Viral loads, antibody titers, symptom scores and body temperature are a few of the outcome variables commonly studied. Longitudinal EI data are inherently nonlinear, often with single-peaked response trajectories with a common pre- and post-infection baseline. Such data are frequently analyzed with statistical methods …

Sobriety In Delta Not Sober, Joe Mashburn

Mathematics Faculty Publications

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

Using Time Series Models For Defect Prediction In Software Release Planning, James W. Tunnell

All Master's Theses

To produce a high-quality software release, sufficient time should be allowed for testing and fixing defects. Otherwise, there is a risk of slip in the development schedule and/or software quality. A time series model is used to predict the number of bugs created during development. The model depends on the previous numbers of bugs created. The model also depends, in an exogenous manner, on the previous numbers of new features resolved and improvements resolved. This model structure would allow hypothetical release plans to be compared by assessing their predicted impact on testing and defect- fixing time. The VARX time series …

Estimation And Identification Of Change Points In Panel Models With Nonstationary Or Stationary Regressors And Error Term, Badi H. Baltagi, Chihwa Kao, Long Liu

Center for Policy Research

This paper studies the estimation of change point in panel models. We extend Bai (2010) and Feng, Kao and Lazarová (2009) to the case of stationary or nonstationary regressors and error term, and whether the change point is present or not. We prove consistency and derive the asymptotic distributions of the Ordinary Least Squares (OLS) and First Difference (FD) estimators. We find that the FD estimator is robust for all cases considered.

Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

Statistics In The Billera-Holmes-Vogtmann Treespace, Grady S. Weyenberg

Theses and Dissertations--Statistics

This dissertation is an effort to adapt two classical non-parametric statistical techniques, kernel density estimation (KDE) and principal components analysis (PCA), to the Billera-Holmes-Vogtmann (BHV) metric space for phylogenetic trees. This adaption gives a more general framework for developing and testing various hypotheses about apparent differences or similarities between sets of phylogenetic trees than currently exists.

For example, while the majority of gene histories found in a clade of organisms are expected to be generated by a common evolutionary process, numerous other coexisting processes (e.g. horizontal gene transfers, gene duplication and subsequent neofunctionalization) will cause some genes to exhibit a …

Preparing Secondary Mathematics Teachers: Focus On Modeling In Algebra, Hyunyi Jung, Alexia Mintos, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study addressed the opportunities to learn (OTL) modeling in algebra provided to secondary mathematics pre-service teachers (PSTs). To investigate these OTL, we interviewed five instructors of required mathematics and mathematics education courses that had the potential to include opportunities for PSTs to learn algebra at three universities. We also interviewed a group of three to four PSTs at each of the universities. We coded the interview transcripts using an analytic framework developed based on related literature and policy documents. We report the similarities and differences in perspectives among instructors and PSTs related to modeling at each university, along with …

Characterizations Of Gamma Distribution Via Sub-Independent Random Variables, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

The concept of sub-independence is based on the convolution of the distributions of the random variables. It is much weaker than that of independence, but is shown to be sufficient to yield the conclusions of important theorems and results in probability and statistics. It also provides a measure of dissociation between two random variables which is much stronger than uncorrelatedness. Inspired by the excellent work of Jin and Lee (2014), we present certain characterizations of gamma distribution based on the concept of sub-independence.

Kumaraswamy-Half-Cauchy Distribution: Characterizations And Related Results, Gholamhossein Hamedani, I. Ghosh

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present various characterizations of a recently introduced distribution (Ghosh 2014), called Kumaraswamy- Half- Cauchy distribution based on: (i) a simple relation between two truncated moments; (ii) truncated moment of certain function of the 1^st order statistic; (iii) truncated moment of certain function of the random variable; (iv) hazard function; (v) distribution of the 1^st order statistic; (vi) via record values. We also provide some remarks on bivariate Gumbel copula distribution whose marginal distributions are Kumaraswamy- Half-Cauchy distributions.

Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin

Masters Theses

"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …

Space-Based Relative Multitarget Tracking, Keith Allen Legrand

Masters Theses

"Access to space has expanded dramatically over the past decade. The growing popularity of small satellites, specifically cubesats, and the following launch initiatives have resulted in exponentially growing launch numbers into low Earth orbit. This growing congestion in space has punctuated the need for local space monitoring and autonomous satellite inspection. This work describes the development of a framework for monitoring local space and tracking multiple objects concurrently in a satellite's neighborhood. The development of this multitarget tracking systems has produced collateral developments in numerical methods, relative orbital mechanics, and initial relative orbit determination.

This work belongs to a class …

Uncertainty Quantification Of Turbulence Model Closure Coefficients For Transonic Wall-Bounded Flows, John Anthony Schaefer

Masters Theses

"The goal of this work was to quantify the uncertainty and sensitivity of commonly used turbulence models in Reynolds-Averaged Navier-Stokes codes due to uncertainty in the values of closure coefficients for transonic, wall-bounded flows and to rank the contribution of each coefficient to uncertainty in various output flow quantities of interest. Specifically, uncertainty quantification of turbulence model closure coefficients was performed for transonic flow over an axisymmetric bump at zero degrees angle of attack and the RAE 2822 transonic airfoil at a lift coefficient of 0.744. Three turbulence models were considered: the Spalart-Allmaras Model, Wilcox (2006) k-ω Model, and the …

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 …

The Distribution Of Type 1 Diabetes Onset In The United States By Demographic Factors, Margaret Beckstrand

Walden Dissertations and Doctoral Studies

Type 1 diabetes (T1D) is a chronic and lifelong condition, often diagnosed in childhood. Patients with T1D are at elevated risks of associated health complications, comorbidities, and mortality. Occurrence, clinical presentation, and complications related to T1D differ by age of onset, ethnicity, and gender. The last reported population-based estimates regarding the burden of T1D in children using the National Health and Nutrition Examination Survey (NHANES) were published in 2008, and these estimates were not well stratified by age of onset, ethnicity, and gender. The purpose of this study was to examine these demographics within the conceptual framework of the hygiene …

Mahalanobis Kernel-Based Support Vector Data Description For Detection Of Large Shifts In Mean Vector, Vu Nguyen

Electronic Theses and Dissertations

Statistical process control (SPC) applies the science of statistics to various process control in order to provide higher-quality products and better services. The K chart is one among the many important tools that SPC offers. Creation of the K chart is based on Support Vector Data Description (SVDD), a popular data classifier method inspired by Support Vector Machine (SVM). As any methods associated with SVM, SVDD benefits from a wide variety of choices of kernel, which determines the effectiveness of the whole model. Among the most popular choices is the Euclidean distance-based Gaussian kernel, which enables SVDD to obtain a …

Statistical Engineering: A Causal-Stochastic Modeling Research Update, Teddy Steven Cotter

Engineering Management & Systems Engineering Faculty Publications

In the ASEM-IAC 2012, Cotter (2012) summarized prior works that led to the proposal for statistical engineering, identified the gaps in knowledge that statistical engineering needs to address, explored additional gaps in knowledge not addressed in the prior works, set forth a working definition of and body of knowledge for statistical engineering, and set forth proposals of potential systems contributions the Engineering Management profession could make toward the development of statistical engineering. In 2014, the ASQ Statistics Division, DOT&E, NASA, and IDA co-sponsored a Statistical Engineering Agreement to jointly research development of the discipline of statistical engineering. The statistics community …

Modeling The Dynamic Processes Of Challenge And Recovery (Stress And Strain) Over Time, Fan Yang

Department of Statistics: Dissertations, Theses, and Student Research

A dynamic process with challenge and recovery is an important branch in the family of stochastic processes. The dependent data of such processes are often observed over time, and hence, are time dependent. The purpose of this dissertation is to develop methods to characterize a dynamic process with challenge and recovery under different dimensionalities and error assumptions. In this dissertation, a univariate dynamic process under Gaussian assumption is discussed first and a bi-logistic model is developed by three different methods: compartment, additive, and Bayesian. Then the discussion is extended to a bivariate hysteresis system with challenge and recovery. Three methods: …

Investigating Use Of Beta Coefficients For Stock Predictions, Jeffrey Swensen

Williams Honors College, Honors Research Projects

By using previous stock market data, investors can get a good sense of how to invest for the future. A common way to determine what stocks are riskier than others is by using the beta coefficient. This paper investigates the relationship between the overall S&P 500 market and certain individual stocks to see if we can use past stock return data to predict the future riskiness of certain stocks. Correlation between the individual stocks and the S&P 500 will allow us to determine the relationship between the two. Finding the beta coefficients for the individual stock market will allow investors …

Combinatorially Interpreting Generalized Stirling Numbers, John Engbers, David Galvin, Justin Hilyard

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Exponentially Increasing Incidences Of Cutaneous Malignant Melanoma In Europe Correlate With Low Personal Annual Uv Doses And Suggests 2 Major Risk Factors, Stephen Merrill, Samira Ashrafi, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

For several decades the incidence of cutaneous malignant melanoma (CMM) steadily increased in fair-skinned, indoor-working people around the world. Scientists think poor tanning ability resulting in sunburns initiate CMM, but they do not understand why the incidence continues to increase despite the increased use of sunscreens and formulations offering more protection. This paradox, along with lower incidences of CMM in outdoor workers, although they have significantly higher annual UV doses than indoor workers have, perplexes scientists. We found a temporal exponential increase in the CMM incidence indicating second-order reaction kinetics revealing the existence of 2 major risk factors. From epidemiology …

The Transmuted Exponentiated Generalized-G Family Of Distributions, Haitham M. Yousof, Ahmed Z. Afify, Morad Alizadeh, Nadeem Shafique Butt, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a new class of continuous distributions called the transmuted exponentiated generalized-G family which extends the exponentiated generalized-G class introduced by Cordeiro et al. (2013). We provide some special models for the new family. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probability weighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of an applications to real dataset.

Characterizations Of Transmuted Complementary Weibull Geometric Distribution, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We present certain characterizations of a recently introduced distribution (Afify et al., 2014), called Transmuted Complementary Weibull Geometric distribution based on: hazard function ; a simple relation between two truncated moments. We like to mention that the characterization which is expressed in terms of the ratio of truncated moments is stable in the sense of weak convergence. It does not require a closed form for the cumulative distribution function and serves as a bridge between a first order differential equation and probability.

Characterizations Of Nwp, Etgr And Twl Distributions, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Utilizing a simple relationship between two truncated moments as well as certain functions of the 1st and of the nth order statistics, we characterize three extended classes of distributions proposed in (2015).

Characterizations Of Distributions Via Conditional Expectation Of Generalized Order Statistics, M. Ahsanullah, Gholamhossein Hamedani, Mehdi Maadooliat

Mathematics, Statistics and Computer Science Faculty Research and Publications

Characterizations of probability distributions by different regression conditions on generalized order statistics has attracted the attention of many researchers. We present here, characterizations of certain continuous distributions based on the conditional expectation of generalized order statistics.

Signal Processing Spreads A Voxel’S Temporal Frequency Task-Activated Peak And Induces Spatial Correlations In Dual-Task Complex-Valued Fmri, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Characteristics Of Feedback That Influence Student Confidence And Performance During Mathematical Modeling, Hyunyi Jung, Heidi A. Diefes-Dux, Aladar K. Horvath, Kelsey Joy Rodgers, Monica E. Cardella

Mathematics, Statistics and Computer Science Faculty Research and Publications

This study focuses on characteristics of written feedback that influence students’ performance and confidence in addressing the mathematical complexity embedded in a Model-Eliciting Activity (MEA). MEAs are authentic mathematical modeling problems that facilitate students’ iterative development of solutions in a realistic context. We analyzed 132 first-year engineering students’ confidence levels and mathematical model scores on aMEA(pre and post feedback), along with teaching assistant feedback given to the students. The findings show several examples of affective and cognitive feedback that students reported that they used to revise their models. Students’ performance and confidence in developing mathematical models can be increased when …