Physical Sciences and Mathematics Commons^™

Comparing Performance Of Gene Set Test Methods Using Biologically Relevant Simulated Data, Richard M. Lambert

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Today we know that there are many genetically driven diseases and health conditions. These problems often manifest only when a set of genes are either active or inactive. Recent technology allows us to measure the activity level of genes in cells, which we call gene expression. It is of great interest to society to be able to statistically compare the gene expression of a large number of genes between two or more groups. For example, we may want to compare the gene expression of a group of cancer patients with a group of non-cancer patients to better understand the genetic …

Physically Based Preconditioning Techniques Applied To The First Order Particle Transport And To Fluid Transport In Porous Media, Michael Rigley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Solving linear systems is at the heart of many scientific applications from the PreAlgebra's student solving for x and y for basic geometry problems to the computational scientist solving billions of equations with billions of variables for weather forecasting, modeling fusion reactions, or web search algorithms. In this study we look at improving the efficiency of solving large linear systems that result from two applications. The first includes linear systems that result from solving differential equations for the movement of atomic particles in particle emitting, void, and absorbing regions. The second includes solving linear systems that result from solving differential …

Computational Topics In Lie Theory And Representation Theory, Thomas J. Apedaile

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The computer algebra system Maple contains a basic set of commands for working with Lie algebras and matrices. The purpose of this thesis was to extend the functionality of these Maple packages in a number of important areas. First, programs for defining multiplication in several different types of algebras were created to allow users to perform a wider variety of calculations. Second, commands were created for calculating some basic properties of matrix representations of semisimple Lie algebras. This allows a user to identify a given matrix representation by a collection of integers which do not change when the basis of …

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 hypothesis 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 …

Implementation And Application Of The Curds And Whey Algorithm To Regression Problems, John Kidd

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A common statistical problem is trying to predict two or more variables using a set of predictor variables. The simplest model for this situation is called multivariate linear regression. This method uses each set of predictor variables to predict each of the response variables separately. This approach seems counter-intuitive as any possible relationship between the variables being predicted is ignored.

Breiman and Friedman found a way to take advantage of relationships among the response variables to increase the accuracy of the predictions for each of the predicted variables with an algorithm they called Curds and
Whey. It uses other statistical …

Beetles, Fungi And Trees: A Story For The Ages? Modeling And Projecting The Multipartite Symbiosis Between The Mountain Pine Beetle, Dendroctonus Ponderosae, And Its Fungal Symbionts, Grosmannia Clavigera And Ophiostoma Montium, Audrey L. Addison

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

As data collection and modeling improve, ecologists increasingly discover that interspecies dynamics greatly affect the success of individual species. Models accounting for the dynamics of multiple species are becoming more important. In this work, we explore the relationship between mountain pine beetle (MPB, Dendroctonus ponderosae Hopkins) and two mutualistic fungi, Grosmannia clavigera and Ophiostoma montium. These species are involved in a multipartite symbiosis, critical to the survival of MPB, in which each species benefits.

Extensive phenological modeling has been done to determine how temperature affects the timing of life events and cold-weather mortality of MPB. The fungi have also …

Probability Of Discrete Failures, Weibull Distribution, Mary Jo Hansen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The intent of this research and these is to describe the development of a series of charts and tables that provide the individual and cumulative probabilities of failure applying to the Weibull statistical distribution. The mathematical relationships are developed and the computer programs are described for deterministic and Monte Carlo models that compute and verify the results. Charts and tables reflecting the probabilities of failure for a selected set of parameters of the Weibull distribution functions are provided.

Parameter Estimation For Generalized Pareto Distribution, Der-Chen Lin

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The generalized Pareto distribution was introduced by Pickands (1975). Three methods of estimating the parameters of the generalized Pareto distribution were compared by Hosking and Wallis (1987). The methods are maximum likelihood, method of moments and probability-weighted moments.

An alternate method of estimation for the generalized Pareto distribution, based on least square regression of expected order statistics (REOS), is developed and evaluated in this thesis. A Monte Carlo comparison is made between this method and the estimating methods considered by Hosking and Wallis (1987). This method is shown to be generally superior to the maximum likelihood, method of moments and …

Comparison Of Bootstrap With Other Tests For Several Distributions, Yu-Yu Wong

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper discusses results of a computer simulation to investigate several different tests when sampling several distributions. The hypothesis H₀: μ=0 was tested against H₀: μ≠0, using the usual t-test, trimmed t-test, the Jackkinfe, the Bootstrap and signed-rank test. The p-values and empirical power show that the Bootstrap is as good as the t-test. The Jackknife procedure is too liberal, always obtaining small p-values. The signed-rank is a fairly good test if the data follows the Cauchy Distribution.

Overall Life Satisfaction Of Ileostomates: Conventional Brooke Ileostomy Versus Modified Kock Pouch, Sandra Sisson Briscoe

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis is to analyze various aspects of quality of life and to determine if there is a difference in quality of life offered by a conventional ileostomy versus a continent ileostomy.

An instrument was developed to measure several factors thought to influence quality of life as well as several structural/demographic variables. This instrument was designed for persons with a conventional ileostomy and was modified for persons who had undergone conversion surgery from conventional to continent ileostomy.

Analysis of variance was performed to determine differences in quality of life for persons with a conventional, conversion, or original …

A Test For Determining An Appropriate Model For Accelerated Life Data, Yuan-Who Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for testing the appropriateness of accelerated life model. This method is based upon a polynomial approximation. The parameters are estimated and used for testing the appropriateness of the model.

An example illustrates the polynomial method. Real data are applied for this method. Comparison with another method demonstrates that the polynomial method is much simpler and has comparable accuracy.

A Comparison Of Rank And Bootstrap Procedures For Completely Randomized Designs With Jittering, Feng-Ling Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper discusses results of a computer simulation to investigate the effect of jittering to simulate measurement error. In addition, the classical F ratio, the bootstrap F and the F for ranked data are compared. Empirical powers and p-values suggest the bootstrap is a good and robust procedure and the rank procedure seems to be too liberal when compared to the classical F ratio.

Nonparametric Confidence Intervals For The Reliability Of Real Systems Calculated From Component Data, Jean Spooner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A methodology which calculates a point estimate and confidence intervals for system reliability directly from component failure data is proposed and evaluated. This is a nonparametric approach which does not require the component time to failures to follow a known reliability distribution.

The proposed methods have similar accuracy to the traditional parametric approaches, can be used when the distribution of component reliability is unknown or there is a limited amount of sample component data, are simpler to compute, and use less computer resources. Depuy et al. (1982) studied several parametric approaches to calculating confidence intervals on system reliability. The test …

Data Analysis Using Experimental Design Model Factorial Analysis Of Variance/Covariance (Dmaovc.Bas), Wesley E. Newton

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

DMAOVC.BAS is a computer program written in the compiler version of microsoft basic which performs factorial analysis of variance/covariance with expected mean squares. The program accommodates factorial and other hierarchical experimental designs with balanced sets of data. The program is writ ten for use on most modest sized microprocessors, in which the compiler is available. The program is parameter file driven where the parameter file consists of the response variable structure, the experimental design model expressed in a similar structure as seen in most textbooks, information concerning the factors (i.e. fixed or random, and the number of levels), and necessary …

Unbalanced Analysis Of Variance Comparing Standard And Proposed Approximation Techniques For Estimating The Variance Components, James P. Pugsley

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This paper considers the estimation of the components of variation for a two-factor unbalanced nested design and compares standard techniques with proposed approximation procedures. Current procedures are complicated and assume the unbalanced sample size to be fixed. This paper tests some simpler techniques, assuming sample sizes are random variables. Monte Carlo techniques were used to generate data for testing of these new procedures.

Correction Of Bias In Estimating Autocovariance Function, Len-Hong Wu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to evaluate a method for reducing the bias of estimation for autocovariance estimators. Two methods are compared, one is the standard method and the other is an adjustment method. The Monte Carlo method is used within comparison.

The bias and the mean squared error of the estimated autocovariance is computed for several time series models and two variations of the adjustment method of estimation. The results indicate some improvement in bias and mean squared error for the new method.

The Use Of Contingency Table Analysis As A Robust Technique For Analysis Of Variance, Mei-Eing Chiu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper is to compare Analysis of Variance with Contingency Table Analysis when the data being analyzed do not satisfy Analysis of Variance assumptions. The criteria for comparison are the powers of the Standard variance-ratio and the Chi-square test.

The test statistic and powers were obtained by Monte Carlo.

1. Calculate test statistic for each of 100 trials, this process was repeated 12 times. Each time different combination of means and variances were used.

2. Powers were obtained for each of 12 combinations of means and variances.

Whether Analysis of Variance or Contingency Table Analysis is a …

Parameter Estimation In Nonstationary M/M/S Queueing Models, Pensri Vajanaphanich

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

If either the arrival rate or the service rate in an M/M/S queue exhibit variability over time, then no steady state solution is available for examining the system behavior. The arrival and service rates can be represented through Fourier series approximations. This permits numerical approximation of the system characteristics over time.

An example of an M/M/S representation of the operations of emergency treatment at Logan Regional hospital is presented. It requires numerical integration of the differential equation for L(t), the expected number of customers in the system at time t.

Linear Regression Of The Poisson Mean, Duane Steven Brown

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis was to compare two estimation procedures, the method of least squares and the method of maximum likelihood, on sample data obtained from a Poisson distribution. Point estimates of the slope and intercept of the regression line and point estimates of the mean squared error for both the slope and intercept were obtained. It is shown that least squares, the preferred method due to its simplicity, does yield results as good as maximum likelihood.

Also, confidence intervals were computed by Monte Carlo techniques and then were tested for accuracy. For the method of least squares, confidence …

Least Squares Estimation Of The Pareto Type I And Ii Distribution, Ching-Hua Chien

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The estimation of the Pareto distribution can be computationally expensive and the method is badly biased. In this work, an improved Least Squares derivation is used and the estimation will be less biased. Numerical examples and figures are provided so that one may observe the solution more clearly. Furthermore, by varying the different methods of estimation, a comparing of the estimators of the parameters is given. The improved Least Squares derivation is confidently employed for it is economic and efficient.

Explanation Of The Fast Fourier Transform And Some Applications, Alan Kazuo Endo

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This report describes the Fast Fourier Transform and some of its applications. It describes the continuous Fourier transform and some of its properties. Finally, it describes the Fast Fourier Transform and its applications to hurricane risk analysis, ocean wave analysis, and hydrology.

Evaluation Of Multivariate Homogenous Arma Model, Lucy Chienhua Tseng

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this thesis is to study a restricted multivariate AFRMA model, called the Homogeneous Model. This model is defined as one in which each univariate component of the multivariate model is of the same order in p and q as it is in the multivariate model.

From a mathematical respect, multivariate ARMA model is homogeneous if, and only if, its coefficient matrices are diagonal. From a physical respect, the present observation of a phenomenon can be modeled only by its own past observation and its present and past "errors."

The estimation procedures are developed based on maximum likelihood …

Extreme Value Distribution In Hydrology, Bill (Tzeng-Lwen) Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The problems encountered when empirical fit is used as the sole criterion for choosing a distribution to represent annual flood data are discussed. Some theoretical direction is needed for this choice. Extreme value theory is established as a viable tool for analyzing annual flood data. Extreme value distributions have been used in previous analyses of flood data. However, no systematic investigation of the theory has previously been applied. Properties of the extreme value distributions are examined. The most appropriate distribution for flood data has not previously been fit to such data. The fit of the chosen extreme value distribution compares …

A Confidence Interval Estimate Of Percentile, How Coung Jou

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The confidence interval estimate of percentile and its applications were studied. The three methods of estimating a confidence interval were introduced. Some properties of order statistics were reviewed. The Monte Carlo Method -- used to estimate the confidence interval was the most important one among the three methods. The generation of ordered random variables and the estimation of parameters were discussed clearly. The comparison of the three methods showed that the Monte Carlo method would always work, but the K-S and the simplified methods would not.

Exact Analysis Of Variance With Unequal Variances, Noriaki Yanagi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this paper was to present the exact analysis of variance with unequal variances. Bishop presented the new procedure for the r-way layout ANOVA. In this paper, one and two way layout ANOVA were explained and Bishop's method and Standard method were compared by using a Monte Carlo method.

The Prior Distribution In Bayesian Statistics, Kai-Tang Chen

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A major problem associated with Bayesian estimation is selecting the prior distribution. The more recent literature on the selection of the prior is reviewed. Very little of a general nature on the selection of the prior is formed in the literature except for non-informative priors. This class of priors is seen to have limited usefulness. A method of selecting an informative prior is generalized in this thesis to include estimation of several parameters using a multivariate prior distribution. The concepts required for quantifying prior information is based on intuitive principles. In this way, it can be understood and controlled by …

Estimation Of Floods When Runoff Originates From Nonhomogeneous Sources, David Ray Olson

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Extreme value theory is used as a basis for deriving a distribution function for flood frequency analysis when runoff originates from nonhomogeneous sources. A modified least squares technique is used to estimate the parameters of the distribution function for eleven rivers. Goodness-of-fit statistics are computed and the distribution function is found to fit the data very well.

The derived distribution function is recommended as a base method for flood frequency analysis for rivers exhibiting nonhomogeneous sources of runoff if further investigation also proves to be positive.

A Μ-Model Approach On The Cell Means: The Analysis Of Full, Design Models With Non-Orthogonal Data, Richard Van Koningsveld

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This work considers the application of a µ-model approach on the cell means to a special yet important class of experimental designs. These include full factorial, completely nested, and mixed models with one or more observations per cell. By limiting attention to full models, an approach to the general data situation is developed which is both conceptually simple and computationally advantageous.

Conceptually, the method is simple because the design related effects are defined as if the cell means are single observations. This leads to a rather simple algorithm for generating main effect contrasts, from which associated interaction contrasts can also …

Interpretation Of Principal Components, Marwan A. Dabdoub

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The principal component analysis can be carried out two ways. First the R-mode:

R = K'K

and the second is the Q-mode:

Q = K K'

where K is a data matrix centered by column or by row. The most commonly used method is the R-mode.

It has been suggested that principal components computed from either the R-mode or the Q-mode may have the same interpretation. If this is true, then interpretation of the principal components could be put on a much more intuitive level in many applications. This will occur whenever one type of principal component …

Multicollinearity And The Estimation Of Regression Coefficients, John Charles Teed

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The precision of the estimates of the regression coefficients in a regression analysis is affected by multicollinearity. The effect of certain factors on multicollinearity and the estimates was studied. The response variables were the standard error of the regression coefficients and a standarized statistic that measures the deviation of the regression coefficient from the population parameter.

The estimates are not influenced by any one factor in particular, but rather some combination of factors. The larger the sample size, the better the precision of the estimates no matter how "bad" the other factors may be.

The standard error of the regression …