Physical Sciences and Mathematics Commons^™

Stressors Across The Lifespan And Dementia Risk: A Statistical Method Analysis, Megan Platt Borrowman

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

The Cache Lifespan Stressors and Alzheimer's Disease (LSAD) study has access to data from the Cache County Study on Memory Health and Aging (CCS) that have been linked to the extensive genealogical and vital records from the Utah Population Database (UPDB). Information about stressful life events experienced by the original 5092 CCS participants has been extracted objectively from the UPDB, without the possibility of recall bias. This information was then statistically analyzed to look for relationships between key stressors and dementia risk. The LSAD study made it possible to examine the correlation between stressors as well as look at patterns …

Collecting, Analyzing And Interpreting Bivariate Data From Leaky Buckets: A Project-Based Learning Unit, Florence Funmilayo Obielodan

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

Despite the significance and the emphasis placed on mathematics as a subject and field of study, achieving the right attitude to improve students‟ understanding and performance is still a challenge. Previous studies have shown that the problem cuts across nations around the world, both developing countries and developed alike. Teachers and educators of the subject have responsibilities to continuously develop innovative pedagogical approaches that will enhance students‟ interests and performance. Teaching approaches that emphasize real life applications of the subject have become imperative. It is believed that this will stimulate learners‟ interest in the subject as they will be able …

Climate Change And Community Dynamics: A Hierarchical Bayesian Model Of Resource-Driven Changes In A Desert Rodent Community, Glenda M. Yenni

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

Predicting effects of climate change on species persistence often assumes that those species are responding to abiotic effects alone. However, biotic interactions between community members may affect species’ ability to respond to abiotic changes. Latent Gaussian models of resource availability using precipitation and NDVI and accounting for spatial autocorrelation and rodent group-level uncertainty in the process are developed to detect differences in seasons, groups, and the experimental removal of one group. Precipitation and NDVI have overall positive effects on rodent energy use as expected, but meaningful differences were detected. Differences in the importance of seasonality when the dominant group was …

Estimation Of Beta In A Simple Functional Capital Asset Pricing Model For High Frequency Us Stock Data, Yan Zhang

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

This project applies the methods of functional data analysis (FDA) to intra-daily returns of US corporations. It focuses on an extension of the Capital Asset Pricing Model (CAPM) to such returns. The CAPM is essentially a linear regression with the slope coefficient β. Returns of an asset are regressed on index return. We compare the estimates of β obtained for the daily and intra-daily returns. The variability of these estimates is assessed by two bootstrap methods. All computations are performed using statistical software R. Customized functions are developed to process the raw data, estimate the parameters and assess their variability. …

Controlling Error Rates With Multiple Positively-Dependent Tests, Abdullah Al Masud

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

It is a typical feature of high dimensional data analysis, for example a microarray study, that a researcher allows thousands of statistical tests at a time. All inferences for the tests are determined using the p-values; a smaller p-value than the α-level of the test signifies a statistically significant test. As the number of tests increases, the chance of observing some small p-values is very high even when all null hypotheses are true. Consequently, we make wrong conclusions on the hypotheses. This type of potential problem frequently happens when we test several hypotheses simultaneously, i.e., the multiple testing problem. …

On The Use Of Log-Transformation Vs. Nonlinear Regression For Analyzing Biological Power-Laws, Xiao Xiao

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

Power-law relationships are among the most well-studied functional relationships in biology . Recently the common practice of fitting power-laws using linear regression on log-transformed data (LR) has been criticized, calling into question the conclusions of hundreds of studies. It has been suggested that nonlinear regression (NLR) is preferable, but no rigorous comparison of these two methods has been conducted. Using Monte Carlo simulations we demonstrate that the error distribution determines which method performs better, with LR better characterizing data with multiplicative lognormal error and NLR better characterizing data with additive normal error. Analysis of 471 biological power-laws shows that both …

Development And Implementation Of A Bayesian Model For Sediment Transport In Fluvial Systems, Mark Schmelter

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

Recent studies in the field of fluvial sediment transport underscore the difficulty in reliably estimating transport model parameters, collecting accurate observations, and making predictions due to measurement error and conceptual model uncertainty. There is a pressing need to develop models that can account for measurement error, conceptual model uncertainty, and natural variability while providing probability-based predictions as well as a means for conceptual model discrimination. The model presented in this research employs an excess shear sediment transport equation for a uni-size sediment bed developed in a Bayesian statistical framework. This statistical model provides a means to rigorously estimate distributions of …

Virtual Manipulatives In The Classroom And Resulting Articles And Lesson Plans, Cheryl Juliana

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

Upon coming across mathematical manipulatives generated and produced by Utah State University, as a math teacher, I conducted a classroom teaching experiment in three pre-algebra classes with students of various achievement levels. After teaching the entire year using no manipulatives in the classroom, I tested my students with a general, end-of-year, core criterion, or cumulative test. Their scores were noted. The students in the study group were then given opportunities to try several manipulatives offered on the "National Library of Virtual Manipulatives," both as a class, and alone, and then retested. The following paper gives the parameters of the study, …

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 …

Improving Accuracy Of Large-Scale Prediction Of Forest Disease Incidence Through Bayesian Data Reconciliation, Ephraim M. Hanks

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

Increasing the accuracy of predictions made from ecological data typically involves replacing or replicating the data, but the cost of updating large-scale data sets can be prohibitive. Focusing resources on a small sample of locations from a large, less accurate data set can result in more reliable observations, though on a smaller scale. We present an approach for increasing the accuracy of predictions made from a large-scale eco logical data set through reconciliation with a small, highly accurate data set within a Bayesian hierarchical modeling framework. This approach is illustrated through a study of incidence of eastern spruce dwarf mistletoe …

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 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.

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 …

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.

Statistical Analysis Of Wastewater Remediation And Bio-Fuels Production Of Algae, Jay D. Jones

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

The Logan city wastewater treatment system consists of a series of seven large aerated ponds (460 acres) that biologically treats 15 million gallons per day of wastewater from Logan city and six other communities. Tighter regulations of allowed phosphorus levels in the effluent have recently been implemented due to environmental concerns of a downstream reservoir. The Biological Engineering program at Utah State University, the Bio-fuels Center, the Utah Water Research Laboratory (UWRL) and the city of Logan are working together to remediate the wastewater treatment system using microalgae. Algal growth requires the uptake of phosphorus. Thus, phosphorus in the effluent …

Theory Of Planned Behavior Model Fit Using Atod Prevention Program Data, Ying Jin

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

This report is to test the Theory of Planned Behavior (TpB) model fit using the data collected from the ATOD Prevention Program conducted by the Operation Snowball Program from year 2004 to 2007 in Naperville, Illinois. Measurement Model and Structural Equation Modeling are used as principal modeling methods to test internal consistency of assigned measures for each construct and the dependency between constructs respectively. The results show that the ATOD Prevention Program data does not fit the TpB model perfectly. Extra paths should be added to the original theoretical model in order to obtain a satisfactory model fit.

The Effectiveness Of Institutional Intervention At Minimizing Demographic Inertia And Improving The Representation Of Women Faculty In Higher Education, Amanda V. Bakian

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

Across all science and engineering disciplines, women currently receive 46% of the doctoral degrees granted annually. Despite gains in doctoral degrees earned by women over the past 30 years, they remain under-represented among full time tenured /tenure-track science and engineering faculty compared to their presence among degree recipients. The inequality gap is widest among full professors at 4 year research universities where women account for a mere 16% of all S&E full time full professors. Multiple hypothesis have been proposed to account for women's under-representation relative to men including those based on human capital/economic theory, feminist theory, innate biological gender …

Logistic Models With Missing Categorical Covariates, Jeremiah Rounds

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

We present an EM based solution to missing categorical covariates in Binomial models with logit links using an assumption that experimental units are drawn from a Multinomial population of infinite size. We further address the problem of separation of points inducing large variances on parameter estimates by the use of a novel score-modification based on Firth's bias-reduction score-modification. We simulate to address questions about estimate bias, distribution, and appropriate parameter coverage by Wald intervals.

Approaches To Promote Active, Conceptual Learning In A Pedagogically Hybrid Introductory Statistics Course, Brittany L. Allred

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

Statistics education is an active area of research where discovery-based learning is becoming more prominent. This project reviews how the USEI and GAISE recommendations can be implemented in the statistics classroom. Further, the project describes the creation of a library of classroom materials for an introductory statistics course. The results are also discussed from implementing various library materials, along with the student response to hands-on learning techniques.

The Statistical Evaluation Of Collective Risk Models With Various Distributional Assumptions, Chang Li

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

Our thesis includes 2 sections. In section 1, we mainly discuss the distribution function and the empirical simulation of the total claims amount for a portfolio with multiple distributional assumptions, under the collective risk model for a single period.

In section 2, we discuss the collective risk model for an extended period, which mainly deals with the amount of surplus over several periods of time. Let Un denote the surplus at time n, then we interested in the probability of ruin, that is, the probability that there exists an n such that Un< O. In this section, we put forward an algorithm for the probability of ruin (both theoretical and empirical) using this model, with various distributional assumptions, and compare the theoretical and empirical results.

The reference of this project is Actuarial …

Probe-Level Statistical Models For Differential Expression Of Genes In Bovine Nt Studies, Jason L. Bell

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

A brief introduction of microarray technology and its uses is given. This technology is commonly used in agricultural research, including research in nuclear transfer, which motivated this study. There are 3 classes of statistical models compared: probeset-level, weighted probeset-level and probe-level.

Different statistical mod els are compared on 3 spike-in experiments to assess the relative performance in identifying differentially expressed genes . A novel nested factorial model was found to outperform all other models compared in this study in one spike-in experiment, and was found to be competitive in its performance relative to the other models on the other spike-in …

Comparison Of Random Forests And Cforest: Variable Importance Measures And Prediction Accuracies, Rong Xia

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

Random forests are ensembles of trees that give accurate predictions for regression, classification and clustering problems. The CART tree, the base learn er employed by random forests, has been criticized because of bias in the selection of splitting variables. The performance of random forests is suspect due to this criticism. A new implementation of random forests, Cforest, which is claimed to outperform random forests in both predictive power and variable importance measures , was developed based on Ctree, an implementation of conditional inference trees.

We address the underlying mechanism of random forests and Cforest in this report. Comparison of random …

An Investigation Of The Ends Of Finitely Generated Groups, Daniel T. Murphree

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

Geometric group theory is a relatively new branch of mathematics, studied as a distinct area since the 1990's. It explores invariant properties of groups based on group actions defined on topological or geometrical spaces. One of the pioneering works in geometric group theory is the article "Topological Methods in Group Theory" by Peter Scott and Terry Wall, written in 1977. This article was an overview of revised notes from an advanced course give in Liverpool in the same year. This report is an attempt to make these notes more accessible to lower level graduate students in the fields of topology …

Applications Of Modern Classification Methods To Predict Occurrences Of Rare And Invasive Plant Species, Stacey Reynolds

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

Statistical classification methods are among the most widely used statistical procedures in ecology. Applications include vegetation mapping by remote sensing (Steele 2000), discrimination of subspecies using morphological measurements (Fisher 1936, 1938; Conner and Schenk 2003), and species distribution modelling (Guisan and Zimmerman 2000). Examples of the last application abound in the ecological literature and include predicting the distribution or characteristics of plant species (see, e.g., Austin et al. 1990), predicting presence and absence aquatic biota in streams (Hawkins et al. 2000), and habit at relationships of terrestrial animal species (Welch and MacMahon 2005). Over the last 20 years two mainstays …

Cow Insurance Vs. Human Insurance: A Comparison Study, Corlan Fawcett

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

This paper will compare the premiums to insure cows and humans for n-year term, n-year endowment, and whole life insurance. It will go into more depth for whole life premium s that would be charged, such that the insurance company is 95 percent confident that they will not lose money. In particular the paper will look at how the variance affects the premiums for an insurance company insuring 100 cows.

Evaluating The Effectiveness Of A Probability Applet, Chelsa Green Tuddenham

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

The purpose of this project was to develop and examine a computerized interactive probability applet designed to teach basic concepts of probability. The applet design was intended to be a user-friendly way to encourage understanding of basic probability concepts such as, rules of probability, probabilities of mutually exclusive events, and the multiplication rule. Thirty participants were recruited from Utah State University and were asked to participate in the evaluation process of the probability applet. The evaluation of the probability applet consisted of three parts: First, a group of participants were video recorded and asked to voice any and all thoughts …

Comparison Of Exact Methods For Analyzing Family-Based Samples, Abbie Lundgreen

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

Family-based association tests are used to identify genes that increase the risk of developing a disease, while controlling for spurious associations caused by population structure. The exact family-based association test, exact FBAT, is a unified approach which can be app lied to tests of different genetic models, sampling designs, null hypotheses , and missing parental information.

The purpose of this report is to compare the power of the exact FBAT with two other tests, exact conditional logistic regression (CLR) and the exact trend test for clustered data (QEM). Pedigrees of sibships were simulated based upon a variety of different parameters, …

A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas

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

Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).

A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

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

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …