Statistics and Probability Commons^™

Approximate Vs. Monte Carlo Critical Values For The Winsorized T-Test, Michael Lance

Wayne State University Dissertations

Historically, it has been accepted practice for critical values for the Winsorized t test for independent samples to be based on adjusted degrees of freedom depending on the number of total non-Winsorized (approximate) values. Recently, a new such table of Winsorized critical values has been developed via approximate randomization by Monte Carlo simulation.

Based on eight common data distributions estimated from Psychology and Education along with the normal and five Mathematical distributions, these two tables of values were compared with respect to robustness to types I and II errors through Monte Carlo simulations for one and 10% Winsorized values per …

A Comparison Of The Effects Of Non-Normal Distributions On Tests Of Equivalence, Linda Ellington

Wayne State University Dissertations

Statistical theory and its application provide the foundation to modern systematic inquiry in the behavioral, physical and social sciences disciplines (Fisher, 1958; Wilcox, 1996). It provides the tools for scholars and researchers to operationalize constructs, describe populations, and measure and interpret the relations between populations and variables (Weinbach & Grinnell, 1997; Wilcox, 1996). Given that the majority of real data analysis in the behavioral and social sciences is comprised of non-normally distributed data, it is important that researchers be aware of the effects of non-normal distributions on the probability of detecting equivalence between populations.

The present study examined the effects …

An Analog Experiment Comparing Goal-Free Evaluation And Goal Achievement Evaluation Utility, Brandon W. Youker

Dissertations

Goal-free evaluation (GFE) is the process of determining the merit of an evaluand independent of the stated or implied goals and objectives, whereas goal achievement evaluation (GAE), as the most rudimentary form of goal-based evaluation, determines merit according to the evaluand’s level of accomplishment with regard to its goals. This study examines the utility of GAE and GFE from the perspective of the evaluation’s intended users. In the study, two evaluation teams, goal achievement and goal-free, independently and simultaneously evaluate the same human service program. Each team produced a final evaluation report, which was read by the evaluation’s users, who …

Class Discovery And Prediction Of Tumor With Microarray Data, Bo Liu

All Graduate Theses, Dissertations, and Other Capstone Projects

Current microarray technology is able take a single tissue sample to construct an Affymetrix oglionucleotide array containing (estimated) expression levels of thousands of different genes for that tissue. The objective is to develop a more systematic approach to cancer classification based on Affymetrix oglionucleotide microarrays. For this purpose, I studied published colon cancer microarray data. Colon cancer, with 655,000 deaths worldwide per year, has become the fourth most common form of cancer in the United States and the third leading cause of cancer - related death in the Western world. This research has been focuses in two areas: class discovery, …

Assessing Measurement Invariance In The Presence Of Testlets, Luis Andres Alvarado

Open Access Theses & Dissertations

Dealing with measurement invariance has been an issue of concern in confirmatory factor analysis for many years. It is important to establish measurement invariance across groups so that instruments may be validly used in multiple groups for comparison of the mean or summative scores. Throughout the years, many studies have considered testing for measurement invariance in factor models. However, there have been no studies that assess measurement invariance when so-called testlets should be modeled in the factor analytic model. Testlets add nuisance covariation to the model which can interfere when trying to detect measurement invariance. In the past, models have …

A Proposed Epithermal Model For The High Grade District, California, Michael Nicholas Feinstein

Open Access Theses & Dissertations

A historic gold mining district in northeastern California has not been incorporated into the global knowledge base for precious metal vein deposits. This study collected various data types which are important characteristics in the classification and understanding of vein deposits. The High Grade District (HGD) is a gold mining site located in the northeast corner of Modoc County, California, in the Warner Mountains. The Warner Mountains are composed of Tertiary eruptive centers, cropping out between valleys formed through extensional tectonics. Mineralization of the HGD displays abundant silicification, adularia, and gold; these characteristics are sufficient to classify mineralization as low-sulfidation epithermal …

Bayesian Computational Methods For Hidden Markov Models, Samson Laine Ghebremariam

Open Access Theses & Dissertations

Hidden Markov Models (HMMs) have been applied to many real-world problems. Hidden Markov modeling has recently become increasingly important and popular among researchers,and many software tools are based on them. Given that the models are rich in mathematical structure, they can form theoretical foundation for use in a wide range of applications. Hidden Markov models provide a universal configuration for statistical analysis of a large variety of DNA sequences containing symbols A, C, G, T. In a HMM, it is impossible to figure out what state the model is in by just having a look at the symbol generated.

A …

Distributional Properties Of Inversions And Segmentation Algorithms For Rna Sequences, Sameera Dhananjaya Viswakula

Open Access Theses & Dissertations

Ribonucleic acid (RNA) is a long single stranded molecule made up of four types of nucleotide bases: Adenine (A), Cytosine(C), Guanine (G) and Uracil (U). It folds back on itself and forms C-G and A-U complementary base pairs. The set of such hydrogen-bonded pairs in an RNA molecule is called its secondary structure. Knowing the secondary structure of RNA is useful for understanding its biological function. Prediction of RNA secondary structure from the nucleotide sequence has been an important bioinformatics problem for over two decades.

The work in this thesis is motivated by the need to improve the secondary structure …

Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …

Gamma And Generalized Gamma Distributions, Victor Hugo Jiménez Nava

Open Access Theses & Dissertations

We present the Generalized Gamma Distribution, study its properties and derive the estimators of the parameters. This distribution includes many standard forms, like: Gamma, Exponential, Weibull, Half Normal and others. Sum and ratios of independent generalized gamma lead to intractable forms. However approximation works well. In particular two-moment gamma and three moment normal approximations are shown to approximate the sum of k independent gamma as well as generalized gamma distributions.

Principal Differential Analysis With Covariates : A Simulation Study On The Effect Of The Smoothing Parameters, Indika Varuna Mallawaarachchi

Open Access Theses & Dissertations

Principal Differential Analysis deals with functional data. The word functional data refers to a collection of curves that are independent and measured on a dense grid of time points in an interval. These time points can be equally or unequally spaced. A differential equation is believed capable of capturing the features of these n curves.

Ramsay(1996) first introduced Principal Differential Analysis (PDA) as an alternative to the Principal Component Analysis(PCA). PDA finds a linear differential equation that captures features of a collection of curves, in order to have a low dimensional approximation for functional data. PDA is based on the …

Computational Methods Of Hidden Markov Models With Respect To Cpg Island Prediction In Dna Sequences, Roberto Angel Ortega

Open Access Theses & Dissertations

Hidden Markov models (HMM's) are a specific case of Markov models where, contrary to Markov chains, the observer is unaware of what state the model was in when the symbol is observed. Like Markov chains, HMM's assume that the future state of a sequence is dependent only on the current state of the sequence. The parameters associated with HMM's are transition and emission probabilities, where transition probabilities are associated with the probability of transitioning from one state to another, and emission probabilities are the probabilities associated with observing a symbol given it came from a specific state.

The structure of …

Estimating The Effect Of Dust And Low Wind Events On Hospitalizations For Asthma While Adjusting For Hourly Levels Of Air Pollutants, Priyangi Kanchana Bulathsinhala

Open Access Theses & Dissertations

El Paso, Texas is known as one of the dust hotspots in North America. We explore the effect of dust and low wind events on asthma admissions in El Paso, Texas between 2000 and 2005. Conditional logistic regression with a case-crossover design was used to estimate the probability of hospitalization after dust and low wind events while controlling for pollutants with hourly monitor measurements, and weather. The historical functional linear model is used to incorporate the hourly pollutant measures into the regression model with a continuous lag, as an alternative to a distributed lag model based on daily averages. The …

Estimating The Reproductive Numbers For The 2008-2009 Cholera Outbreaks In Zimbabwe, Zindoga Mukandavire, Shu Liao, Jin Wang, Holly Gaff, David L. Smith, J. Glenn Morris Jr.

Biological Sciences Faculty Publications

Cholera remains an important global cause of morbidity and mortality, capable of causing periodic epidemic disease. Beginning in August 2008, a major cholera epidemic occurred in Zimbabwe, with 98,585 reported cases and 4,287 deaths. The dynamics of such outbreaks, particularly in nonestuarine regions, are not well understood. We explored the utility of mathematical models in understanding transmission dynamics of cholera and in assessing the magnitude of interventions necessary to control epidemic disease. Weekly data on reported cholera cases were obtained from the Zimbabwe Ministry of Health and Child Welfare (MoHCW) for the period from November 13, 2008 to July 31, …

Meta-Analysis Of Single-Case Data: A Monte Carlo Investigation Of A Three Level Model, Corina M. Owens

USF Tampa Graduate Theses and Dissertations

Numerous ways to meta-analyze single-case data have been proposed in the literature, however, consensus on the most appropriate method has not been reached. One method that has been proposed involves multilevel modeling. This study used Monte Carlo methods to examine the appropriateness of Van den Noortgate and Onghena's (2008) raw data multilevel modeling approach to the meta-analysis of single-case data. Specifically, the study examined the fixed effects (i.e., the overall average baseline level and the overall average treatment effect) and the variance components (e.g., the between person within study variance in the average baseline level, the between study variance in …

Parent Involvement In Children's Schooling: An Investigation Of Measurement Equivalence Across Ethnic Groups, Heather Marie Scott

USF Tampa Graduate Theses and Dissertations

Epstein et al.'s Theory of Overlapping Spheres of Influence focuses on the interaction and communication, or partnerships, among families, schools, and the community to bring the three closer together. The theory works in conjunction with Epstein's typology of parental involvement, which focuses on six types of involvement that are instrumental to a child's development and his/her school and educational success. These serve as the framework for the study and support the construct of parent's involvement in children's schooling.

The purpose of the current study was to conduct further validation analyses of an inventory designed to measure the construct of parent …

Statistical Analysis And Modeling: Cancer, Clinical Trials, Environment And Epidemiology., Dimitrios Vovoras

USF Tampa Graduate Theses and Dissertations

The current thesis is structured in four parts. Vector smoothing methods are used to study environmental data, in particular records of extreme precipitation, the models utilized belong to the vector generalized additive class. In the statistical analysis of observational studies the identification and adjustment for prognostic factors is an important component of the analysis; employing flexible statistical methods to identify and characterize the effect of potential prognostic factors in a clinical trial, namely "generalized additive models", presents an alternative to the traditional linear statistical model. The classes of models for which the methodology gives generalized additive extensions include grouped survival …

Modeling Endogenous Treatment Eects With Heterogeneity: A Bayesian Nonparametric Approach, Xuequn Hu

USF Tampa Graduate Theses and Dissertations

This dissertation explores the estimation of endogenous treatment effects in the presence of heterogeneous responses. A Bayesian Nonparametric approach is taken to model the heterogeneity in treatment effects. Specifically, I adopt the Dirichlet Process Mixture (DPM) model to capture the heterogeneity and show that DPM often outperforms Finite Mixture Model (FMM) in providing more flexible function forms and thus better model fit. Rather than fixing the number of components in a mixture model, DPM allows the data and prior knowledge to determine the number of components in the data, thus providing an automatic mechanism for model selection.

Two DPM models …

Modeling And Analysis Of Repeated Ordinal Data Using Copula Based Likelihoods And Estimating Equation Methods, Raghavendra Rao Kurada

Mathematics & Statistics Theses & Dissertations

Repeated or longitudinal ordinal data occur in many fields such as biology, epidemiology, and finance. These data normally are analyzed using both likelihood and non-likelihood methods. The first part of this dissertation discusses the multivariate ordered probit model which is a likelihood method based on latent variables. We show that this latent variable model belong to a very general class of Copula models. We use the copula representation for the multivariate ordered probit model to obtain maximum likelihood estimates of the parameters. We apply the methodology in the analysis of real life data examples.

Though likelihood methods are preferable, there …

Why Is An Einstein Ring Blue?, Jonathan Blackledge

Articles

Albert Einstein predicted the existence of `Einstein rings' as a consequence of his general theory of relativity. The phenomenon is a direct result of the idea that if a mass warps space-time then light (and other electromagnetic waves) will be `lensed' by the strong gravitational field produced by a large cosmological body such as a galaxy. Since 1998, when the first complete Einstein ring was observed, many more complete or partially complete Einstein rings have been observed in the radio and infrared spectra, for example, and by the Hubble Space Telescope in the optical spectrum. However, in the latter case, …

Analysis Of Differential Gene Expression And Alternative Splicing In The Liver And Gastrointestinal Tract In The Lactating Rat, Antony Thomas Athippozhy

University of Kentucky Doctoral Dissertations

Rat exon microarrays were utilized to detect changes in mRNA expression and alternative splicing in the liver, duodenum, jejunum, and ileum of the lactating rat when compared to age-matched virgin controls. Analysis of data at the level of gene expression revealed differential expression of genes involved in cholesterol biosynthesis in each tissue examined, suggesting increased Sterol Response Element Binding Protein activity. We also detected decreased mRNA from components of the T-cell signaling pathway in the jejunum and ileum. We characterized expression of solute carrier and adenosine triphosphate binding cassette proteins. In addition to characterizing genes by pathway, we have also …

Neurological And Cardiovascular Outcomes After Cardiac Arrest At Six Regional Interventional Cardiology Centers In The United States 2007-2011, David B. Seder Md, Nainesh Patel Md, John Mcpherson Md, Paul W. Mcmullan Md, Karl B. Kern Md, Barbara Unger Rn, J Browning, Sudip Nanda Md, Facp, Melkon Hacobian Md, Michael B. Kelley Md, Niklas Nielsen Md, Phd, Michael R. Mooney Md

Department of Medicine

No abstract provided.

Post-Resuscitation Care Practices Following Cardiac Arrest At Six Regional Interventional Cardiology Centers In The United States 2007-2011, David B. Seder Md, Nainesh Patel Md, John A. Mcpherson Md, Paul W. Mcmullan Md, Karl B. Kern Md, Barbara T. Unger Rn, J Browning, Sudip Nanda Md, Facp, Melkon Hacobian Md, Michael B. Kelley Md, Niklas Nielsen Md, Phd, Michael R. Mooney Md

Department of Medicine

No abstract provided.

Geriatric Experience Following Cardiac Arrest At Six Interventional Cardiology Centers In The United States 2007-2011, David B. Seder Md, Nainesh Patel Md, John A. Mcpherson Md, Paul W. Mcmullan Md, Karl B. Kern Md, Barbara T. Unger Rn, J Browning, Sudip Nanda Md, Facp, Melkon Hacobian Md, Michael B. Kelley Md, Niklas Nielsen Md, Phd, Michael R. Mooney Md

Department of Medicine

No abstract provided.

Robustness Analysis Of Slow Learning In Iterative Learning Control Systems, John R. Singler, Douglas A. Bristow

Mechanical and Aerospace Engineering Faculty Research & Creative Works

This paper examines robust stability and robust transient growth in Iterative Learning Control (ILC). It is well known that small perturbations in system dynamics can result in very large transient growth of some ILC systems. Even larger perturbations can result in instability. One ad hoc technique commonly employed to improve robustness is to slow the learning rate by reducing the learning filter gain or lowpass filtering the error signal. Here, pseudospectra analysis is used to analyze the robustness of ILC algorithms with slow learning. It is found that robustness bounds can be increased and transient growth decreased with decreasing learning …

Computational Network Analysis Of The Anatomical And Genetic Organizations In The Mouse Brain, Shuiwang Ji

Computer Science Faculty Publications

Motivation: The mammalian central nervous system (CNS) generates high-level behavior and cognitive functions. Elucidating the anatomical and genetic organizations in the CNS is a key step toward understanding the functional brain circuitry. The CNS contains an enormous number of cell types, each with unique gene expression patterns. Therefore, it is of central importance to capture the spatial expression patterns in the brain. Currently, genome-wide atlas of spatial expression patterns in the mouse brain has been made available, and the data are in the form of aligned 3D data arrays. The sheer volume and complexity of these data pose significant challenges …

The Doubly Inflated Poisson And Related Regression Models, Manasi Sheth-Chandra

Mathematics & Statistics Theses & Dissertations

Most real life count data consists of some values that are more frequent than allowed by the common parametric families of distributions. For data consisting of only excess zeros, in a seminal paper Lambert (1992) introduced Zero-Inflated Poisson (ZIP) model, which is a mixture model that accounts for the inflated zeros. In this thesis, two Doubly Inflated Poisson (DIP) probability models, DIP (p, λ) and DIP ( p1, p2, λ), are discussed for situations where there is another inflated value k > 0 besides the inflated zeros. The distributional properties such as identifiability, moments, and conditional probabilities …

Identifying Rare Variants From Exome Scans: The Gaw17 Experience, Saurabh Ghosh, Heike Bickeboller, Julia Bailey, Joan E. Bailey-Wilson, Rita Cantor, Robert Culverhouse, Warwick Daw, Anita L. Destefano, Corinne D. Engelman, Anthony Hinrichs, Jeanine Houwing-Duistermaat, Inke R. Konig, Jack Kent, Nan Laird, Nathan Pankratz, Andrew Paterson, Elizabeth Pugh, Brian Suarez, Yan Sun, Alun Thomas, Nathan L. Tintle, Xiaofeng Zhu, Andreas Ziegler, Jean W. Maccluer, Laura Almasy

Faculty Work Comprehensive List

Genetic Analysis Workshop 17 (GAW17) provided a platform for evaluating existing statistical genetic methods and for developing novel methods to analyze rare variants that modulate complex traits. In this article, we present an overview of the 1000 Genomes Project exome data and simulated phenotype data that were distributed to GAW17 participants for analyses, the different issues addressed by the participants, and the process of preparation of manuscripts resulting from the discussions during the workshop

Some Contributions To The Censored Empirical Likelihood With Hazard-Type Constraints, Yanling Hu

University of Kentucky Doctoral Dissertations

Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. Owen’s 2001 book contains many important results for EL with uncensored data. However, fewer results are available for EL with right-censored data. In this dissertation, we first investigate a right-censored-data extension of Qin and Lawless (1994). They studied EL with uncensored data when the number of estimating equations is larger than the number of parameters (over-determined case). We obtain results similar to theirs for the maximum EL estimator and the EL ratio test, for the over-determined case, with right-censored data. We employ hazard-type constraints which are better able …

Bayesian Semiparametric Generalizations Of Linear Models Using Polya Trees, Angela Schoergendorfer

University of Kentucky Doctoral Dissertations

In a Bayesian framework, prior distributions on a space of nonparametric continuous distributions may be defined using Polya trees. This dissertation addresses statistical problems for which the Polya tree idea can be utilized to provide efficient and practical methodological solutions.

One problem considered is the estimation of risks, odds ratios, or other similar measures that are derived by specifying a threshold for an observed continuous variable. It has been previously shown that fitting a linear model to the continuous outcome under the assumption of a logistic error distribution leads to more efficient odds ratio estimates. We will show that deviations …