Statistics and Probability Commons^™

Effect Of Noise In Principal Component Analysis With An Application To Ozone Pollution, Katerina G. Tsakiri

Legacy Theses & Dissertations (2009 - 2024)

This thesis analyzes the effect of independent noise in principal components of k normally distributed random variables defined by a covariance matrix. We prove that the principal components as well as the canonical variate pairs determined from joint distribution of original sample affected by noise can be essentially different in comparison with those determined from the original sample. However when the differences between the eigenvalues of the original covariance matrix are sufficiently large compared to the level of the noise, the effect of noise in principal components and canonical variate pairs proved to be negligible. The theoretical results are supported …

The Joint Distribution Of Bivariate Exponential Under Linearly Related Model, Norou Diawara, Kumer Pial Das

Mathematics & Statistics Faculty Publications

In this paper, fundamental results of the joint distribution of the bivariate exponential distributions are established. The positive support multivariate distribution theory is important in reliability and survival analysis, and we applied it to the case where more than one failure or survival is observed in a given study. Usually, the multivariate distribution is restricted to those with marginal distributions of a specified and familiar lifetime family. The family of exponential distribution contains the absolutely continuous and discrete case models with a nonzero probability on a set of measure zero. Examples are given, and estimators are developed and applied to …

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Mathematics Faculty Publications

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.

Coarsening In High Order, Discrete, Ill-Posed Diffusion Equations, Catherine Kublik

Mathematics Faculty Publications

We study the discrete version of a family of ill-posed, nonlinear diffusion equations of order 2n. The fourth order (n=2) version of these equations constitutes our main motivation, as it appears prominently in image processing and computer vision literature. It was proposed by You and Kaveh as a model for denoising images while maintaining sharp object boundaries (edges). The second order equation (n=1) corresponds to another famous model from image processing, namely Perona and Malik's anisotropic diffusion, and was studied in earlier papers. The equations studied in this paper are high order analogues of the Perona-Malik equation, and like the …

Racial/Ethnic Health Disparities In Northeast Ohio, Mark Salling, Joseph Ahern

All Maxine Goodman Levin School of Urban Affairs Publications

Racial/Ethnic Health Disparities in Northeast Ohio, Planning & Action, The Center for Community Solutions, Vol. 63, No. 4 (July), 2010, pp. 12-15.

Putting Artists On The Map: A Five Part Study Of Greater Cleveland Artists' Location Decisions - Part 1: Summary Report, Mark Salling, Gregory Soltis, Charles Post, Sharon Bliss, Ellen Cyran

All Maxine Goodman Levin School of Urban Affairs Publications

A series of reports detailing the residential and work space location preferences of Cuyahoga county's artists.

Census 2010 And Human Services And Community Development, Mark Salling, Jenita Mcgowan

All Maxine Goodman Levin School of Urban Affairs Publications

Census 2010 and Human Services and Community Development, Planning & Action, The Center for Community Solutions, Vol. 63, No. 2 (March), 2010, pp 1-4.

Statistical Topology Via Morse Theory, Persistence And Nonparametric Estimation, Peter Bubenik, Gunnar Carlsson, Peter T. Kim, Zhiming Luo

Mathematics and Statistics Faculty Publications

In this paper we examine the use of topological methods for multivariate statistics. Using persistent homology from computational algebraic topology, a random sample is used to construct estimators of persistent homology. This estimation procedure can then be evaluated using the bottleneck distance between the estimated persistent homology and the true persistent homology. The connection to statistics comes from the fact that when viewed as a nonparametric regression problem, the bottleneck distance is bounded by the sup-norm loss. Consequently, a sharp asymptotic minimax bound is determined under the sup–norm risk over H¨older classes of functions for the nonparametric regression problem on …

Numerical Solution Of The Five-Moment Ideal Two-Fluid Equations In One Dimension, Marcus Scott

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

Plasmas are frequently treated as a single conducting fluid and modeled using the equations of magnetohydrodynamics. However, this regime works better for low-frequency plasmas. High-frequency plasmas may be modeled using the principles of kinetic theory. For plasmas with frequencies between these two extremes, a two-fluid approach can yield better results. In 2006, Ammar Hakim mathematically modeled a plasma with a set of equations called the five-moment ideal two-fluid equations. An attempt is made reproduce those results. A derivation of this set of equations by taking moments of the Boltzmann equation is presented. Electric and magnetic fields contribute to the source …

Assessing North American Influenza Dynamics With Hierarchical Spatio-Temporal Models, Jessica Anderson

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

We present a general statistical modeling framework to characterize continental-level influenza dynamics in the United States for the purposes of examining state-level epidemiological sources and sinks. The methods we describe depend directly on state-level influenza data that are updated weekly and available on the internet. Advances in search engine query analysis have provided powerful new tools for collecting epidemiological data and, when used in conjunction with sophisticated statistical models, allow for the identification and quantification of the flow of influenza across the continental United States. Our proposed methods, when conditioned on this comprehensive search query product, can provide unprecedented scientific …

A Comparison Of Prediction Methods Of Functional Autoregressive Time Series, Devin Didericksen

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

Functional data analysis (FDA) is a relatively new branch of statistics that has seen a lot of expansion recently. With the advent of computer processing power and more efficient software packages we have entered the beginning stages of applying FDA methodology and techniques to data. Part of this undertaking should include an empirical assessment of the effectiveness of some of the tools of FDA, which are sound on theoretical grounds. In a small way, this project helps advance this objective.

This work begins by introducing FDA, scalar prediction techniques, and the functional autoregressive model of order one - FAR(1). Two …

Assessing The Precision And Accuracy In A Small Sample Of Actical Devices, Peter Sherick

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

Actigraphy is an increasingly popular approach in medicine to assess patient activity levels in a variety of scenarios. The devices are essentially accelerometers encased in a write-watch type assembly. This project sought to determine the device precision and accuracy for the Actical model. In a sample of four Acticals, it was found that intra-device variability was minimal. However, one device was found to be statistically biased in comparison to the other three. This bias could have adverse effects on aggregated or magnitude dependent data analysis. Also, inter-device comparisons may be problematic.

Assessment Of Utah Bankruptcies By Census Tracts: A Spatial Statistical Approach, Kenneth Pena

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

There are two questions raised when looking at the spatial pattern of the rate of bankruptcies in Utah: (i) are there similarities between the bankruptcy data in adjacent census tracts and (ii) can local cluster and outliers be identified within the data? Specifically, are there similar rates of bankruptcies in bordering census tracts and are there any localized areas of interest where we find extremely high or extremely low rates of bankruptcies? This study uses spatial statistics to perform tests for spatial autocorrelation to address these two questions. It also looks at commonalities in the clusters and differences in the …

Simulating Power For One-Way Anova By Using Non-Normal Error Distributions, Caixia Xu

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

Usually we assume that the distribution of the additive errors in a one-way ANOVA linear model is normal. However, exceptions to this assumption about the error distribution may exist. In such cases, we might consider non-normal error distributions, but proceed with the "usual" ANOVA F-test analyses. This study focuses on simulating power for one-way ANOVA when using non-normal error distributions.

A New Perspective On Visual Word Processing Efficiency, Joseph W. Houpt, James T. Townsend

Psychology Faculty Publications

As a fundamental part of our daily lives, visual word processing has received much attention in the psychological literature. Despite the well established perceptual advantages of word and pseudoword context using accuracy, a comparable effect using response times has been elusive. Some researchers continue to question whether the advantage due to word context is perceptual. We use the capacity coefficient, a well established, response time based measure of efficiency to provide evidence of word processing as a particularly efficient perceptual process to complement those results from the accuracy domain.

Some Problems Of Outliers In Circular Data., Ali H.M. Abuzaid

Student Works (2010-2019)

This study considers three problems of outliers in circular statistics. The first problem is an attempt to use the standard outlier detection procedures for linear data set by approximating circular variables by linear variables. This is possible for large values of concentration parameter. Series of simulation studies are carried out to specify the accepted value of the concentration parameter so that the von Mises distribution can be approximated by normal distribution. The second is the problem of outliers in circular samples. Two numerical tests of discordancy are proposed to identify outliers. The test statistics are based on the summation of …

Character Degrees Of Normally Monomial Maximal Class 5-Groups, Michael Slattery

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper will impose limits on the possible sets of irreducible character degrees of a normally monomial 5-group of maximal class.

Developing Preservice Teachers’ Mathematical And Pedagogical Knowledge Using An Integrated Approach, Marta Magiera, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper describes how an integrated mathematics content and early field-experience course provides opportunities for preservice elementary teachers to develop understanding of mathematics and mathematics teaching. Engaging preservice teachers in solving and discussing mathematical tasks and providing opportunities to implement these tasks with elementary students creates an authentic context for the future teachers to reflect on their own understanding of mathematics, mathematics teaching, and students’ mathematical thinking. Essential elements of the cycle of events in the integrated model of instruction are discussed: preservice students’ acquisition of mathematical concepts in the context of selected tasks in the content course; subsequent posing …

Gliomapredict: A Clinically Useful Tool For Assigning Glioma Patients To Specific Molecular Subtypes, Aiguo Li, Serdar Bozdag, Yuri Kotliarov, Howard A. Fine

Mathematics, Statistics and Computer Science Faculty Research and Publications

Background: Advances in generating genome-wide gene expression data have accelerated the development of molecular-based tumor classification systems. Tools that allow the translation of such molecular classification schemas from research into clinical applications are still missing in the emerging era of personalized medicine.

Results: We developed GliomaPredict as a computational tool that allows the fast and reliable classification of glioma patients into one of six previously published stratified subtypes based on sets of extensively validated classifiers derived from hundreds of glioma transcriptomic profiles. Our tool utilizes a principle component analysis (PCA)-based approach to generate a visual representation of the analyses, quantifies …

Nonparametric Estimation Of Derivatives With Applications, Benjamin Hall

University of Kentucky Doctoral Dissertations

We review several nonparametric regression techniques and discuss their various strengths and weaknesses with an emphasis on derivative estimation and confidence band creation. We develop a generalized C(p) criterion for tuning parameter selection when interest lies in estimating one or more derivatives and the estimator is both linear in the observed responses and self-consistent. We propose a method for constructing simultaneous confidence bands for the mean response and one or more derivatives, where simultaneous now refers both to values of the covariate and to all derivatives under consideration. In addition we generalize the simultaneous confidence bands to account for heteroscedastic …