Statistics and Probability Commons^™

Investigating The Ironwood Tree (Casuarina Equisetifolia) Decline On Guam Using Applied Multinomial Modeling, Karl Anthony Schlub

LSU Master's Theses

The ironwood tree (Casuarina equisetifolia), a protector of coastlines of the sub-tropical and tropical Western Pacific, is in decline on the island of Guam where aggressive data collection and efforts to mitigate the problem are underway. For each sampled tree the level of decline was measured on an ordinal scale consisting of five categories ranging from healthy to near dead. Several predictors were also measured including tree diameter, fire damage, typhoon damage, presence or absence of termites, presence or absence of basidiocarps, and various geographical or cultural factors. The five decline response levels can be viewed as categories of a …

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 …

Statistical Modelling And Inference For A Class Of Bivariate And Related Distributions., Ng Choung Min

Student Works (2010-2019)

This thesis considers bivariate extension of the Meixner class of distributions by the method of generalized trivariate reduction so that the marginal distributions have different parameters; in particular, a new bivariate negative binomial (BNB) distribution is examined. Different marginal parameters allow flexibility in statistical modelling and simulation studies when different marginal distributions and a specified correlation are required. The multivariate extension of this class of distributions is also given. Specifically, various interesting properties of the proposed BNB distribution, such as canonical expansion and quadrant dependence are examined. In addition, potential applications of the proposed distribution, as a bivariate mixed Poisson …

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 …

Anomalous Diffusion In Trading Models., Sidiq Mohamad Khidzir

Student Works (2010-2019)

Econophysics is an interdisciplinary research field applying the mathematical methods of statistical physics to economics and finance. It emphasizes quantitative analysis of large amounts of economic and financial data as oppose to the more philosophical approach of political economics. A popular topic studied in econophysics is the distribution of wealth.Many models have been proposed to explain the trading dynamics [12,13] leading to the distribution of wealth universally observed in many countries. A more recent topic in econophysics is the movement of money studied by Brockmann in [19,20]. In this work, we are interested in studying the relation between the distribution …

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.

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 …

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.

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 …

Comparison And Application Of Three Decorrelation Methods Pca, Maf And Acdc, Jacqueline Ferreira

Theses : Honours

Geostatistics is a branch of applied mathematics that deals with spatially correlated data. Analysing and modelling spatially correlated data can be difficult and time consuming, especially for a multivariate data set. One of the techniques used to make analysis and modelling easier involves decorrelation, whereby a linear transformation on the sample variables is used to associate the spatially correlated variables with a set of decorrelated factors which are statistically and spatially independent. PCA was one of the first multivariate techniques and is mostly used as a data reduction technique. A popular alternative decorrelation technique often used in the mining industry …

Impact Of Higher Education Workplace Relations Requirements On Nteu Membership Density, Tulsi Laxman Panchani

Theses : Honours

The National Tertiary Education Union (NTEU) is the only union working entirely in tertiary education around Australia. The union has over twenty four thousand members comprising of academic and general staff. NTEU maintains membership records at three levels, national, state and branch. The information collected includes gender, age group, employment type and work classification. In late April 2005, Higher Education Workplace Relations Requirements (HEWRRs) legislation was introduced by the Australian government. This legislation imposed restrictions on the interaction between the universities and the union and also curtailed an automatic involvement of the union in the resolution of workplace issues. The …

Linear Dependency For The Difference In Exponential Regression, Indika Sathish, Norou Diawara

Mathematics & Statistics Faculty Publications

In the field of reliability, a lot has been written on the analysis of phenomena that are related. Estimation of the difference of two population means have been mostly formulated under the no-correlation assumption. However, in many situations, there is a correlation involved. This paper addresses this issue. A sequential estimation method for linearly related lifetime distributions is presented. Estimations for the scale parameters of the exponential distribution are given under square error loss using a sequential prediction method. Optimal stopping rules are discussed using concepts of mean criteria, and numerical results are presented.

Probability Models For Blackjack Poker, Charlie H. Cooke

Mathematics & Statistics Faculty Publications

For simplicity in calculation, previous analyses of blackjack poker have employed models which employ sampling with replacement. in order to assess what degree of error this may induce, the purpose here is to calculate results for a typical hand where sampling without replacement is employed. It is seen that significant error can result when long runs are required to complete the hand. The hand examined is itself of particular interest, as regards both its outstanding expectations of high yield and certain implications for pair splitting of two nines against the dealer's seven. Theoretical and experimental methods are used in order …