Statistics and Probability Commons^™

Robust Estimation Of The Correlation Matrix Of Longitudinal Data, Mehdi Maadooliat, Mohsen Pourahmadi, Jianhua Z. Huang

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose a double-robust procedure for modeling the correlation matrix of a longitudinal dataset. It is based on an alternative Cholesky decomposition of the form Σ=DLL ^⊤ D where D is a diagonal matrix proportional to the square roots of the diagonal entries of Σ and L is a unit lower-triangular matrix determining solely the correlation matrix. The first robustness is with respect to model misspecification for the innovation variances in D, and the second is robustness to outliers in the data. The latter is handled using heavy-tailed multivariate t-distributions with unknown degrees of freedom. We …

Considerations In Designing Human-Computer Interfaces For Elderly People, Drew Williams, Mohammad Arif Ul Alam, Sheikh Iqbal Ahamed, William Chu

Mathematics, Statistics and Computer Science Faculty Research and Publications

As computing devices continue to become more heavily integrated into our lives, proper design of human-computer interfaces becomes a more important topic of discussion. Efficient and useful human-computer interfaces need to take into account the abilities of the humans who will be using such interfaces, and adapt to difficulties that different users may face – such as the difficulties that elderly users must deal with. Interfaces that allow for user-specific customization, while taking into account the multiple difficulties that older users might face, can assist the elderly in properly using these newer computing devices, and in doing so possibly achieving …

The Zografos-Balakrishnan Log-Logistic Distribution: Properties And Applications, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Rssi Based Indoor Localization For Smartphone Using Fixed And Mobile Wireless Node, Md O. Gani, Casey O'Brien, Sheikh Iqbal Ahamed, Roger O. Smith

Mathematics, Statistics and Computer Science Faculty Research and Publications

Nowadays with the dispersion of wireless networks, smartphones and diverse related services, different localization techniques have been developed. Global Positioning System (GPS) has a high rate of accuracy for outdoor localization but the signal is not available inside of buildings. Also other existing methods for indoor localization have low accuracy. In addition, they use fixed infrastructure support. In this paper, we present a novel system for indoor localization, which also works well outside. We have developed a mathematical model for estimating location (distance and direction) of a mobile device using wireless technology. Our experimental results on Smartphones (Android and iOS) …

How Ideas Grow: Critical Mass In The Linear Threshold Model, Hossein Alidaee

Mathematics, Statistics, and Computer Science Honors Projects

We study how ideas spread through a social network using the Linear Threshold Model. Each node i on the complete graph K_n is given a threshold Ɵ_i chosen uniformly at random from (0, 1]. This threshold indicates the fraction of the social network that must be active (or believe the idea) prior to node i becoming active. We start with an activated group of early adopters, called the seed set. Considering various scenarios, we use the probabilistic method to find lower bounds on size of a seed set which guarantees that all nodes become active with high …

Simplicial Complexes Obtained From Qualitative Probability Orders, Paul H. Edelman, Tatiana Gvozdeva, Arkadii Slinko

Vanderbilt Law School Faculty Publications

The goal of this paper is to introduce a new class of simplicial complexes that naturally generalize the threshold complexes. These will be derived from qualitative probability orders on subsets of a finite set that generalize subset orders induced by probability measures. We show that this new class strictly contains the threshold complexes and is strictly contained in the shifted complexes. We conjecture that this class of complexes is exactly the set of strongly acyclic complexes, a class that has previously appeared in the context of cooperative games. Beyond the results themselves, this new class of complexes allows us to …

Creating A User Satisfaction Index From A Parsimonious Survey Instrument, Brian Barthel

All Graduate Theses, Dissertations, and Other Capstone Projects

In this paper we present a comprehensive method for creating a user satisfaction index using a survey instrument. First we construct a parsimonious survey instrument, using the PageRank Centrality, to measure attributes of user satisfaction. Then confirmatory factor analysis is applied to extract ``weights'' on the questions that are used in a linear model of computing the user satisfaction index. Throughout the paper an analysis of an existing data set is implemented to illustrate the proposed method. In addition the validity of the confirmatory factor model is tested using bootstrap sampling.

Optimization In Non-Parametric Survival Analysis And Climate Change Modeling, Iuliana Teodorescu

USF Tampa Graduate Theses and Dissertations

Many of the open problems of current interest in probability and statistics involve complicated data

sets that do not satisfy the strong assumptions of being independent and identically distributed. Often,

the samples are known only empirically, and making assumptions about underlying parametric

distributions is not warranted by the insufficient information available. Under such circumstances,

the usual Fisher or parametric Bayes approaches cannot be used to model the data or make predictions.

However, this situation is quite often encountered in some of the main challenges facing statistical,

data-driven studies of climate change, clinical studies, or financial markets, to name a few. …

Oscillation Results For Fourth-Order Nonlinear Dynamic Equations, Chenghui Zhang, Tongxing Li, Ravi P. Agarwal, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

This work is concerned with the oscillation of a certain class of fourth-order nonlinear dynamic equations on time scales. a new oscillation result and an example are included. © 2012 Elsevier Ltd. All rights reserved.

Jensen's Functionals On Time Scales, Matloob Anwar, Rabia Bibi, Martin Bohner, Josip Pečarić

Mathematics and Statistics Faculty Research & Creative Works

We consider Jensen's functionals on time scales and discuss its properties and applications. Further, we define weighted generalized and power means on time scales. by applying the properties of Jensen's functionals on these means, we obtain several refinements and converses of Hölder's inequality on time scales. Copyright © 2012 Matloob Anwar et al.

G-Cimp Status Prediction Of Glioblastoma Samples Using Mrna Expression Data, Mehmet Baysan, Serdar Bozdag, Margaret C. Cam, Svetlana Kotliarova, Susie Ahn, Jennifer Walling, Jonathan K. Killian, Holly Stevenson, Paul Meltzer, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Glioblastoma Multiforme (GBM) is a tumor with high mortality and no known cure. The dramatic molecular and clinical heterogeneity seen in this tumor has led to attempts to define genetically similar subgroups of GBM with the hope of developing tumor specific therapies targeted to the unique biology within each of these subgroups. Recently, a subset of relatively favorable prognosis GBMs has been identified. These glioma CpG island methylator phenotype, or G-CIMP tumors, have distinct genomic copy number aberrations, DNA methylation patterns, and (mRNA) expression profiles compared to other GBMs. While the standard method for identifying G-CIMP tumors is based on …

The Sense-Isomorphism Theoretical Image Voxel Estimation (Sense-Itive) Model For Reconstruction And Observing Statistical Properties Of Reconstruction Operators, Iain P. Bruce, M. Muge Karaman, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

The acquisition of sub-sampled data from an array of receiver coils has become a common means of reducing data acquisition time in MRI. Of the various techniques used in parallel MRI, SENSitivity Encoding (SENSE) is one of the most common, making use of a complex-valued weighted least squares estimation to unfold the aliased images. It was recently shown in Bruce et al. [Magn. Reson. Imag. 29(2011):1267-1287] that when the SENSE model is represented in terms of a real-valued isomorphism,it assumes a skew-symmetric covariance between receiver coils, as well as an identity covariance structure between voxels. In this manuscript, we show …

On Lattices Of Varieties Of Restriction Semigroups, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

The left restriction semigroups have arisen in a number of contexts, one being as the abstract characterization of semigroups of partial maps, another as the ‘weakly left E-ample’ semigroups of the ‘York school’, and, more recently as a variety of unary semigroups defined by a set of simple identities. We initiate a study of the lattice of varieties of such semigroups and, in parallel, of their two-sided versions, the restriction semigroups. Although at the very bottom of the respective lattices the behaviour is akin to that of varieties of inverse semigroups, more interesting features are soon found in the …

Well Conditioned Boundary Integral Equations For Two-Dimensional Sound-Hard Scattering Problems In Domains With Corners, Akash Anand, Jeffrey S. Ovall, Catalin Turc

Mathematics and Statistics Faculty Publications and Presentations

We present several well-posed, well-conditioned direct and indirect integral equation formulations for the solution of two-dimensional acoustic scattering problems with Neumann boundary conditions in domains with corners. We focus mainly on Direct Regularized Combined Field Integral Equation (DCFIE-R) formulations whose name reflects that (1) they consist of combinations of direct boundary integral equations of the second-kind and first-kind integral equations which are preconditioned on the left by coercive boundary single-layer operators, and (2) their unknowns are physical quantities, i.e., the total field on the boundary of the scatterer. The DCFIE-R equations are shown to be uniquely solvable in appropriate function …

An Impulsive Delay Differential Inequality And Applications, Xiaodi Li, Martin Bohner

Mathematics and Statistics Faculty Research & Creative Works

An impulsive delay differential inequality is formulated in this paper. an estimate of the rate of decay of solutions to this inequality is obtained. It can be applied to the study of dynamical behavior of delay differential equations from the impulsive control point of view. as an application, we consider a class of impulsive control systems with time-varying delays and establish a sufficient condition to guarantee the global exponential stability. It is shown that, via proper impulsive control law, a linear delay differential system can be exponentially stabilized even if it is initially unstable. a numerical example is given to …

Mathematical Problem Posing As A Measure Of Curricular Effect On Students' Learning, Jinfa Cai, John Moyer, Ning Wang, Stephen Hwang, Bikai Nie, Tammy Garber

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show evidence of strengths one might expect of students who used the standards-based reform curriculum but also bolster the feasibility and validity of problem posing as a measure of curriculum effect on student learning. In addition, the findings of this study demonstrate the usefulness of …

On Order Statistics For Gs-Distributions, M. M. Mohie El-Din, M. M. Amein, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this article, a class of distributions is used to establish several recurrence relations satisfied by single and product moments of order statistics and progressive Type-II right censoring. The recurrence relations for moments of some specific distributions including uniform (a, b); exponential (λ); generalized exponential (α, λ, ν); beta (1, b); beta (b, 1); logistic (α, β) and other distributions from order statistics and progressive Type-II right censoring can be obtained as special cases. A short explanation of GS-distribution can be found in reference [27]. As an example, means, variances and covariances …

H-Coloring Tori, John Engbers, David Galvin

Mathematics, Statistics and Computer Science Faculty Research and Publications

For graphs G and H, an H-coloring of G is a function from the vertices of G to the vertices of H that preserves adjacency. H-colorings encode graph theory notions such as independent sets and proper colorings, and are a natural setting for the study of hard-constraint models in statistical physics. We study the set of H-colorings of the even discrete torus View the MathML source, the graph on vertex set {0,…,m−1}d (m even) with two strings adjacent if they differ by 1 (mod m) on one coordinate and agree on all others. This is a bipartite graph, with bipartition …

Analyzing Multiple-Probe Microarray: Estimation And Application Of Gene Expression Indexes, Mehdi Maadooliat, Jianhua Z. Huang, Jianhua Hu

Mathematics, Statistics and Computer Science Faculty Research and Publications

Gene expression index estimation is an essential step in analyzing multiple probe microarray data. Various modeling methods have been proposed in this area. Amidst all, a popular method proposed in Li and Wong (2001) is based on a multiplicative model, which is similar to the additive model discussed in Irizarry et al. (2003a) at the logarithm scale. Along this line, Hu et al. (2006) proposed data transformation to improve expression index estimation based on an ad hoc entropy criteria and naive grid search approach. In this work, we re-examined this problem using a new profile likelihood-based transformation estimation approach that …

Role Of Glutathione In Lung Retention Of 99mtc-Hexamethylpropyleneamine Oxime In Two Unique Rat Models Of Hyperoxic Lung Injury, Said H. Audi, David L. Roerig, Steven Thomas Haworth, Anne V. Clough

Biomedical Engineering Faculty Research and Publications

Rat exposure to 60% O₂ for 7 days (hyper-60) or to >95% O₂ for 2 days followed by a 24-hour in room air (hyper-95R) confers susceptibility or tolerance, respectively, of the otherwise lethal effects of subsequent exposure to 100% O₂. The objective of this study was to determine if lung retention of the radiopharmaceutical agent ^99mTc-HMPAO (hexamethylpropyleneamine oxime) is differentially altered in hyper-60 and hyper-95R rats. Tissue retention of HMPAO is dependent on intracellular content of the antioxidant glutathione (GSH) and mitochondrial function. HMPAO was injected i.v. in anesthetized rats and planar images were acquired. …

An Efficient Second Order In Time Scheme For Approximating Long Time Statistical Properties Of The Two Dimensional Navier-Stokes Equations, Xiaoming Wang

Mathematics and Statistics Faculty Research & Creative Works

We investigate the long-time behavior of the following efficient second order in time scheme for the 2D Navier-Stokes equations in a periodic box: The scheme is a combination of a 2nd-order in time backward-differentiation and a particular explicit Adams-Bashforth treatment of the advection term. Therefore, only a linear constant coefficient Poisson solver is needed at each time step. We prove uniform in time bounds on this scheme in L 2, H per1 and H per2 provided that the time-step is sufficiently small. These time uniform estimates further lead to the convergence of long-time statistics (stationary statistical properties) of the scheme …

Oscillation And Spectral Theory For Linear Hamiltonian Systems With Nonlinear Dependence On The Spectral Parameter, Martin Bohner, Werner Kratz, Roman Šimon Hilscher

Mathematics and Statistics Faculty Research & Creative Works

In this paper, we consider linear Hamiltonian differential systems which depend in general nonlinearly on the spectral parameter and with Dirichlet boundary conditions. Our results generalize the known theory of linear Hamiltonian systems in two respects. Namely, we allow nonlinear dependence of the coefficients on the spectral parameter and at the same time we do not impose any controllability and strict normality assumptions. We introduce the notion of a finite eigenvalue and prove the oscillation theorem relating the number of finite eigenvalues which are less than or equal to a given value of the spectral parameter with the number of …

From Unbiased Numerical Estimates To Unbiased Interval Estimates, Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos

Departmental Technical Reports (CS)

One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution. Of course, since the sample is finite, the estimate X is, in general, different from the actual value x of the corresponding parameter. What we can require is that the corresponding estimate is unbiased, i.e., that the mean value of the difference X - x is equal to 0: E[X] = x. In some problems, unbiased estimates are not possible. We show that in some such problems, it is possible to have interval unbiased estimates, i.e., …

Modeling Daily Power Demand In Southern Kentucky: A Single Household Approach, Craig M. Dickson

Masters Theses & Specialist Projects

In this study, we use a nonparametric technique, locally weighted robust least squares regression (LOESS), to forecast a 24 hour demand profile at the household level and compare it to existing aggregate demand models discussed in literature. Of these aggregate demand models, a quadratic autoregressive model was selected to be used as a basis for comparison with the LOESS forecasts. It was our goal to automate the forecasting process by using the goodness of fit metric, AICCI, for smoothing parameter selection. The statistical workflow was executed using SAS and data was provided by the Glasgow Electric Plant Board of Barren …

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Department of Mathematics: Dissertations, Theses, and Student Research

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to …

Analysis Of Bank Failure And Size Of Assets, Guancun Zhong

UNLV Theses, Dissertations, Professional Papers, and Capstones

The financial health of the banking industry is an important prerequisite for economic stability and growth. Bank failures in the United States have run in cycles largely associated with the collapse of economic bubbles. The number of bank failures has increased dramatically over the last thirty years (Halling and Hayden, 2007). In this thesis, we try to address the following two questions: 1) What is the relationship, if any, between a bank's asset size and its likelihood of failures? 2) How can we use statistical tools to predict the numbers of bank failures in the future? Various modeling techniques are …

Mathematics And The Hunger Games, Michael A. Lewis

Journal of Humanistic Mathematics

The Hunger Games plot features a dystopian future in which twelve outer districts are oppressed by a centralized capital. The story focuses on the heroism of a sixteen-year-old girl named Katniss and how she tries to rise above the oppression that she experiences. It also features a special lottery and other twists that are sources of mathematical interest. This essay focuses on some of the mathematical issues raised by The Hunger Games in an effort to show that this story can be used to teach students (as well as other interested parties) some important concepts from mathematics.

Bayesian Analysis Of Hypothesis Testing Problems For General Population: A Kullback–Leibler Alternative, Naveen K. Bansal, Gholamhossein Hamedani, Ru Sheng

Mathematics, Statistics and Computer Science Faculty Research and Publications

We consider a hypothesis problem with directional alternatives. We approach the problem from a Bayesian decision theoretic point of view and consider a situation when one side of the alternatives is more important or more probable than the other. We develop a general Bayesian framework by specifying a mixture prior structure and a loss function related to the Kullback–Leibler divergence. This Bayesian decision method is applied to Normal and Poisson populations. Simulations are performed to compare the performance of the proposed method with that of a method based on a classical z-test and a Bayesian method based on the …

Response Surface Optimization Of Electron Beam Freeform Fabrication Depositions Using Design Of Experiments, Patricia A. Quigley

Engineering Management & Systems Engineering Theses & Dissertations

The Electron Beam Freeform Fabrication (EBF³ ) System is a material depositing, layer additive technique that produces three dimensional (3D) parts out of a wide range of metals in high vacuum, using an electron beam and wire feedstock. Screening deposition trials on a titanium alloy, Ti-6Al-4V, at the National Aeronautics Space Administration (NASA) revealed selective vaporization of the aluminum content of linear prototypes when subjected to chemical analysis. In this study, the aluminum content, bead height and bead width output responses were analyzed from a systematic study of the effects that the interactions of the EBF³ processing parameters …

Experimental And Computational Validation And Verification Of The Stokes-Darcy And Continuum Pipe Flow Models For Karst Aquifers With Dual Porosity Structure, Xiaolong Hu, Xiaoming Wang, Max Gunzburger, Fei Hua, Yanzhao Cao

Mathematics and Statistics Faculty Research & Creative Works

In our previous study, we developed the Stokes-Darcy (SD) model was developed for flow in a karst aquifer with a conduit bedded in matrix, and the Beavers-Joseph (BJ) condition was used to describe the matrix-conduit interface. We also studied the mathematical well-posedness of a coupled continuum pipe flow (CCPF) model as well as convergence rates of its finite element approximation. in this study, to compare the SD model with the CCPF model, we used numerical analyses to validate finite element discretisation methods for the two models. using computational experiments, simulation codes implementing the finite element discretisations are then verified. Further …