Statistics and Probability Commons^™

Family-Wise Error Rate Control In Quantitative Trait Loci (Qtl) Mapping And Gene Ontology Graphs With Remarks On Family Selection, Garrett Saunders

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One of the great aims of statistics, the science of collecting, analyzing, and interpreting data, is to protect against the probability of falsely rejecting an accepted claim, or hypothesis, given observed data stemming from some experiment. This is generally known as protecting against a Type I Error, or controlling the Type I Error rate. The extension of this protection against Type I Errors to the situation where thousands upon thousands of hypotheses are examined simultaneously is known as multiple hypothesis testing. This dissertation presents an improvement to an existing multiple hypothesis testing approach, the Focus Level method, specific to gene …

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Modeling Asset Volatility Using Various Resources, Isaac G. Blackhurst

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Volatility is of central interest in modern financial econometrics. This thesis evaluates three different methods of measuring volatility.

Statistical Modeling, Exploration, And Visualization Of Snow Water Equivalent Data, James Beguah Odei

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Due to a continual increase in the demand for water as well as an ongoing regional drought, there is an imminent need to monitor and forecast water resources in the Western United States. In particular, water resources in the Intermountain West rely heavily on snow water storage. Thus, the need to improve seasonal forecasts of snowpack and considering new techniques would allow water resources to be more effectively managed throughout the entire water-year. Many available models used in forecasting snow water equivalent (SWE) measurements require delicate calibrations.

In contrast to the physical SWE models most commonly used for forecasting, we …

New Pod Error Expressions, Error Bounds, And Asymptotic Results For Reduced Order Model Of Parabolic Pdes, John R. Singler

Mathematics and Statistics Faculty Research & Creative Works

The derivations of existing error bounds for reduced order models of time varying partialdi erential equations (PDEs) constructed using proper orthogonal decomposition (POD) haverelied on bounding the error between the POD data and various POD projections of that data.Furthermore, the asymptotic behavior of the model reduction error bounds depends on theasymptotic behavior of the POD data approximation error bounds. We consider time varyingdata taking values in two di erent Hilbert spacesHandV, withVH, and prove exactexpressions for the POD data approximation errors considering four di erent POD projectionsand the two di erent Hilbert space error norms. Furthermore, the exact error expressions …

Highly Sensitive Noninvasive Cardiac Transplant Rejection Monitoring Using Targeted Quantification Of Donor-Specific Cell-Free Deoxyribonucleic Acid, Mats Hidestrand, Aoy Tomita-Mitchell, Pip M. Hidestrand, Arnold Oliphant, Mary Goetsch, Karl D. Stamm, Huan-Ling Liang, Chesney Castleberry, D. Woodrow Benson, Gail Stendahl, Pippa Simpson, Stuart Berger, James S. Tweddell, Steven Zangwill, Michael E. Mitchell

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Micro-Environment Causes Reversible Changes In Dna Methylation And Mrna Expression Profiles In Patient-Derived Glioma Stem Cells, Mehmet Baysan, Kevin Woolard, Serdar Bozdag, Gregory Riddick, Svetlana Kotliarova, Margaret C. Cam, Galina I. Belova, Susie Ahn, Wei Zhang, Hua Song, Jennifer Walling, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

In vitro and in vivo models are widely used in cancer research. Characterizing the similarities and differences between a patient's tumor and corresponding in vitro and in vivo models is important for understanding the potential clinical relevance of experimental data generated with these models. Towards this aim, we analyzed the genomic aberrations, DNA methylation and transcriptome profiles of five parental tumors and their matched in vitro isolated glioma stem cell (GSC) lines and xenografts generated from these same GSCs using high-resolution platforms. We observed that the methylation and transcriptome profiles of in vitro GSCs were significantly different from their corresponding …

Global Resource Management Of Response Surface Methodology, Michael Chad Miller

Dissertations and Theses

Statistical research can be more difficult to plan than other kinds of projects, since the research must adapt as knowledge is gained. This dissertation establishes a formal language and methodology for designing experimental research strategies with limited resources. It is a mathematically rigorous extension of a sequential and adaptive form of statistical research called response surface methodology. It uses sponsor-given information, conditions, and resource constraints to decompose an overall project into individual stages. At each stage, a "parent" decision-maker determines what design of experimentation to do for its stage of research, and adapts to the feedback from that research's potential …

Qualitative Behavior Of Solutions Of Difference Equations With Several Oscillating Coefficients, Martin Bohner, George E. Chatzarakis, Ioannis P. Stavroulakis

Mathematics and Statistics Faculty Research & Creative Works

Sufficient conditions which guarantee the convergence of the non-oscillatory solutions or oscillation of all solutions of a difference equation with several deviating arguments and oscillating coefficients are presented. Corresponding difference equations of both retarded and advanced type are studied. Examples illustrating the results are also given. [Media Object not available: see full text.]

Mcdonald Log-Logistic Distribution With An Application To Breast Cancer Data, M. H. Tahir, Muhammad Mansoor, Muhammad Zubair, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We introduce a five-parameter continuous model, called the McDonald log-logistic distribution, to extend the two-parameter log-logistic distribution. Some structural properties of this new distribution such as reliability measures and entropies are obtained. The model parameters are estimated by the method of maximum likelihood using L-BFGS-B algorithm. A useful characterization of the distribution is proposed which does not require explicit closed form of the cumulative distribution function and also connects the probability density function with a solution of a first order differential equation. An application of the new model to real data set shows that it can give consistently better fit …

Oscillatory Behavior Of Solutions Of Third-Order Delay And Advanced Dynamic Equations, Murat Adivar, Elvan Akin, Raegan Higgins

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we consider oscillation criteria for certain third-order delay and advanced dynamic equations on unbounded time scales. A time scale T is a nonempty closed subset of the real numbers. Examples will be given to illustrate some of the results.

Quantifying The Statistical Impact Of Grappa In Fcmri Data With A Real-Valued Isomorphism, Iain P. Bruce, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The interpolation of missing spatial frequencies through the generalized auto-calibrating partially parallel acquisitions (GRAPPA) parallel magnetic resonance imaging (MRI) model implies a correlation is induced between the acquired and reconstructed frequency measurements. As the parallel image reconstruction algorithms in many medical MRI scanners are based on the GRAPPA model, this study aims to quantify the statistical implications that the GRAPPA model has in functional connectivity studies. The linear mathematical framework derived in the work of Rowe , 2007, is adapted to represent the complex-valued GRAPPA image reconstruction operation in terms of a real-valued isomorphism, and a statistical analysis is performed …

When Semi-Monotone Implies Monotone, Paul Bankston

Mathematics, Statistics and Computer Science Faculty Research and Publications

The basic theme of this talk is the extrinsic description of objects by means of morphisms. One way to do this is to say that all monomorphisms from the object are “special” in some way; the dual of this is to single out epimorphisms to the object.

A Linear Iteration Algorithm For A Second-Order Energy Stable Scheme For A Thin Film Model Without Slope Selection, Wenbin Chen, Cheng Wang, Xiaoming Wang, Steven M. Wise

Mathematics and Statistics Faculty Research & Creative Works

We present a linear iteration algorithm to implement a second-order energy stable numerical scheme for a model of epitaxial thin film growth without slope selection. the PDE, which is a nonlinear, fourth-order parabolic equation, is the L 2 gradient flow of the energy d x. the energy stability is preserved by a careful choice of the second-order temporal approximation for the nonlinear term, as reported in recent work (Shen et al. in SIAM J Numer Anal 50:105-125, 2012). the resulting scheme is highly nonlinear, and its implementation is non-trivial. in this paper, we propose a linear iteration algorithm to solve …

A New Method For Ranking Quarterback Fantasy Performance With Assessment Using Distances Between Rankings, Evan Boyd

Theses, Dissertations and Capstones

Each year around the first week of September, NFL fans are fulfilled with the familiar emotions of watching their team compete for the ultimate prize: Fantasy League Championship. No, the NFL did not rename the Super Bowl. To some, this prize is even more personal than if your favorite childhood NFL team were to win the big game in February. To put it simply, the popularity of fantasy football has grown tremendously over time and the opportunity to best your friends, family, coworkers, whomever it may be that attempts to create the greatest fantasy football roster of all time, absolutely …

Oscillation Criteria For Second-Order Dynamic Equations On Time Scales, Ravi P. Agarwal, Martin Bohner, Tongxing Li, Chenghui Zhang

Mathematics and Statistics Faculty Research & Creative Works

Erbe's and Hassan's contributions regarding oscillation criteria are interesting in the development of oscillation theory of dynamic equations on time scales. The objective of this paper is to amend these results. © 2014 Elsevier Ltd. All rights reserved.

Oscillation Of Second-Order P-Laplace Dynamic Equations With A Nonpositive Neutral Coefficient, Martin Bohner, Tongxing Li

Mathematics and Statistics Faculty Research & Creative Works

We establish some new oscillation criteria for a class of second-order p-Laplace dynamic equations with a nonpositive neutral coefficient on a time scale. The results obtained supplement and improved those reported in the literature. © 2014 Elsevier Ltd. All rights reserved.

Multi-Valued Parabolic Variational Inequalities And Related Variational-Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this paper we study multi-valued parabolic variational inequalities involving quasilinear parabolic operators, and multi-valued integral terms over the underlying parabolic cylinder as well as over parts of the lateral parabolic boundary, where the multi-valued functions involved are assumed to be upper semicontinuous only. Note, since lower semicontinuous multi-valued functions allow always for a Carathéodory selection, this case can be considered as the trivial case and therefore will be omitted. Our main goal is threefold: First, we provide an analytical framework and an existence theory for the problems under consideration. Unlike in recent publications on multi-valued parabolic variational inequalities, the …

Asymptotic Behavior Of Nonoscillatory Solutions Of Higher-Order Integro-Dynamic Equations, Martin Bohner, Said Grace, Nasrin Sultana

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we establish some new criteria on the asymptotic behavior of Non oscillatory solutions of higher-order integro-dynamic equations on time scales. © AGH University of Science and Technology Press, Krakow 2014.

Some Dynamic Hardy-Type Inequalities With General Kernel, Martin Bohner, Ammara Nosheen, Josip Pečarić, Awais Younus

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we extend some Hardy-type inequalities with certain kernels to arbitrary time scales. Certain classical and some new integral and discrete inequalities are deduced in seek of applications. © Zagreb Paper JMI-08-12.

Cycle Lengths Of Θ-Biased Random Permutations, Tongjia Shi

HMC Senior Theses

Consider a probability distribution on the permutations of n elements. If the probability of each permutation is proportional to θ^K, where K is the number of cycles in the permutation, then we say that the distribution generates a θ-biased random permutation. A random permutation is a special θ-biased random permutation with θ = 1. The m^th moment of the r^th longest cycle of a random permutation is Θ(n^m), regardless of r and θ. The joint moments are derived, and it is shown that the longest cycles of a permutation can either be positively or …

Adaptive Stochastic Systems: Estimation, Filtering, And Noise Attenuation, Araz Ryan Hashemi

Wayne State University Dissertations

This dissertation investigates problems arising in identification and control of stochastic systems. When the parameters determining the underlying systems are unknown and/or time varying, estimation and adaptive filter- ing are invoked to to identify parameters or to track time-varying systems. We begin by considering linear systems whose coefficients evolve as a slowly- varying Markov Chain. We propose three families of constant step-size (or gain size) algorithms for estimating and tracking the coefficient parameter: Least-Mean Squares (LMS), Sign-Regressor (SR), and Sign-Error (SE) algorithms.

The analysis is carried out in a multi-scale framework considering the relative size of the gain (rate of …

Safety Effect Of Missouri's Strategic Highway Safety Plan: Missouri's Blueprint For Safer Roadways, Mojtaba A. Mohammadi, V. A. Samaranayake, Ghulam H. Bham

Mathematics and Statistics Faculty Research & Creative Works

This study systematically evaluated the changes in motor vehicle crashes that occurred on the Missouri Interstate highway system following the implementation of the Missouri Strategic Highway Safety Plan (MSHSP) between 2004 and 2007. The MSHSP implemented crash injury reduction strategies in enforcement, education, engineering, and public policy. Empirical Bayesian methods were commonly used to evaluate the effects of any change in safety as a result of countermeasures. This paper presents a simple new approach to evaluating the effects of Missouri's safety plans on roadway crashes. For crash data associated with traffic and roadway characteristics, negative binomial regression models were developed …

Performance Modeling And Optimization Techniques For Heterogeneous Computing, Supada Laosooksathit

Doctoral Dissertations

Since Graphics Processing Units (CPUs) have increasingly gained popularity amoung non-graphic and computational applications, known as General-Purpose computation on GPU (GPGPU), CPUs have been deployed in many clusters, including the world's fastest supercomputer. However, to make the most efficiency from a GPU system, one should consider both performance and reliability of the system.

This dissertation makes four major contributions. First, the two-level checkpoint/restart protocol that aims to reduce the checkpoint and recovery costs with a latency hiding strategy in a system between a CPU (Central Processing Unit) and a GPU is proposed. The experimental results and analysis reveals some benefits, …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Mathematics Faculty Publications

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Mathematics Faculty Publications

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.

Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.

Multi-Peak Solutions To Two Types Of Free Boundary Problems, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

We consider the existence of multi-peak solutions to two types of free boundary problems arising in confined plasma and steady vortex pair under conditions on the nonlinearity we believe to be almost optimal. Our results show that the “core” of the solution has multiple connected components, whose boundary called free boundary of the problems consists approximately of spheres which shrink to distinct single points as the parameter tends to zero.

Introduction To Neutrosophic Statistics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Statistics means statistical analysis of population or sample that has indeterminate (imprecise, ambiguous, vague, incomplete, unknown) data. For example, the population or sample size might not be exactly determinate because of some individuals that partially belong to the population or sample, and partially they do not belong, or individuals whose appurtenance is completely unknown. Also, there are population or sample individuals whose data could be indeterminate.

In this book, we develop the 1995 notion of neutrosophic statistics. We present various practical examples. It is possible to define the neutrosophic statistics in many ways, because there are various types of …