The Brigham Young University Women's Volleyball Team recorded and rated all skills (pass, set, attack, etc.) and recorded rally outcomes (point for BYU, rally continues, point for opponent) for the entire 2006 home volleyball season. Only sequences of events occurring on BYU's side of the net were considered. Events followed one of these general patterns: serve-outcome, pass-set-attack-outcome, or block-dig-set-attack-outcome. These sequences of events were assumed to be first-order Markov chains where the quality of each contact depended only explicitly on the quality of the previous contact but not on contacts further removed in the sequence. We represented these sequences in an extensive matrix of transition probabilities where the elements of the matrix were the probabilities of moving from one state to another. The count matrix consisted of the number of times play moved from one transition state to another during the season. Data in the count matrix were assumed to have a multinomial distribution. A Dirichlet prior was formulated for each row of the count matrix, so posterior estimates of the transition probabilities were then available using Gibbs sampling. The different paths in the transition probability matrix were followed through the possible sequences of events at each step of the MCMC process to compute the posterior probability density that a perfect pass results in a point, a perfect set results in a point, and so forth. These posterior probability densities are used to address questions about skill performance in BYU women's volleyball.

A naive approach to filtering for feedback control of dynamic systems that is robust and stable is proposed. Simulations are run on the filters presented to investigate the robustness properties of each filter. Each simulation with the comparison of the filters is carried out using the usual mean squared error. The filters to be included are the classic Kalman filter, Krein space Kalman, two adjustments to the Krein filter with input modeling and a second uncertainty parameter, a newly developed filter called the Naive filter, bias corrected Naive, exponentially weighted moving average (EWMA) Naive, and bias corrected EWMA Naive filter.

Clinical drug trials are costly and time-consuming. Bayesian methods alleviate the inefficiencies in the testing process while providing user-friendly probabilistic inference and predictions from the sampled posterior distributions, saving resources, time, and money. We propose a dynamic linear model to estimate the mean response at each dose level, borrowing strength across dose levels. Our model permits nonmonotonicity of the dose-response relationship, facilitating precise modeling of a wider array of dose-response relationships (including the possibility of toxicity). In addition, we incorporate an adaptive approach to the design of the clinical trial, which allows for interim decisions and assignment to doses based on dose-response uncertainty and dose efficacy. The interim decisions we consider are stopping early for success and stopping early for futility, allowing for patient and time savings in the drug development process. These methods complement current clinical trial design research.

The objective of this project is to fit a sequence of increasingly complex zero-inflated censored regression models to a known data set. It is quite common to find censored count data in statistical analyses of health-related data. Modeling such data while ignoring the censoring, zero-inflation, and overdispersion often results in biased parameter estimates. This project develops various regression models that can be used to predict a count response variable that is affected by various predictor variables. The regression parameters are estimated with Bayesian analysis using a Markov chain Monte Carlo (MCMC) algorithm. The tests for model adequacy are discussed and the models are applied to an observed data set.

This study investigates benefits of in-service training on LDS primary teachers' ability to state an objective, obtain and keep attention, use wait time, incorporate active participation, teach to the multiple intelligences, and employ positive behavior management techniques. Two groups of 30 viewed either a video-tape or read a handout. Pre and post surveys were used to determine mean gain. Using an ANCOVA, comparisons were made of overall mean gain for each group. Results showed participants made a gain of approximately 1/2 point per question on a 4-point scale on the video and the handout (video gain = .6032 p<.01; handout gain = .6264 p<.01). The results of this study support the hypothesis that teachers receiving one in-service will increase their perception of their ability to teach students with special needs.

The need for website administrators to efficiently and accurately detect the presence of web bots has shown to be a challenging problem. As the sophistication of modern web bots increases, specifically their ability to more closely mimic the behavior of humans, web bot detection schemes are more quickly becoming obsolete by failing to maintain effectiveness. Though machine learning-based detection schemes have been a successful approach to recent implementations, web bots are able to apply similar machine learning tactics to mimic human users, thus bypassing such detection schemes. This work seeks to address the issue of machine learning based bots bypassing machine learning-based detection schemes, by introducing a novel unsupervised learning approach to cluster users based on behavioral biometrics. The idea is that, by differentiating users based on their behavior, for example how they use the mouse or type on the keyboard, information can be provided for website administrators to make more informed decisions on declaring if a user is a human or a bot. This approach is similar to how modern websites require users to login before browsing their website; which in doing so, website administrators can make informed decisions on declaring if a user is a human or a bot. An added benefit of this approach is that it is a human observational proof (HOP); meaning that it will not inconvenience the user (user friction) with human interactive proofs (HIP) such as CAPTCHA, or with login requirements

The first part of my thesis is concerned with estimation for longitudinal data using generalized semi-parametric mixed models and multilevel generalized linear mixed models for a binary response. Likelihood based inferences are hindered by the lack of a closed form representation. Consequently, various integration approaches have been proposed. We propose a spherical radial integration based approach that takes advantage of the hierarchical structure of the data, which we call the 2 SR method. Compared to Pinheiro and Chao's multilevel Adaptive Gaussian quadrature, our proposed method has an improved time complexity with the number of functional evaluations scaling linearly in the number of subjects and in the dimension of random effects per level. Simulation studies show that our approach has similar to better accuracy compared to Gauss Hermite Quadrature (GHQ) and has better accuracy compared to PQL especially in the variance components. The second part of my thesis is concerned with identifying differentially expressed gene pathways/gene sets. We propose a logistic kernel machine to model the gene pathway effect with a binary response. Kernel machines were chosen since they account for gene interactions and clinical covariates. Furthermore, we established a connection between our logistic kernel machine with GLMMs allowing us to use ideas from the GLMM literature. For estimation and testing, we adopted Clarkson's spherical radial approach to perform the high dimensional integrations. For estimation, our performance in simulation studies is comparable to better than Bayesian approaches at a much lower computational cost. As for testing of the genetic pathway effect, our REML likelihood ratio test has increased power compared to a score test for simulated non-linear pathways. Additionally, our approach has three main advantages over previous methodologies: 1) our testing approach is self-contained rather than competitive, 2) our kernel machine approach can model complex pathway effects and gene-gene interactions, and 3) we test for the pathway effect adjusting for clinical covariates. Motivation for our work is the analysis of an Acute Lymphocytic Leukemia data set where we test for the genetic pathway effect and provide confidence intervals for the fixed effects.

The purpose of this study was to estimate the level of statistical power demonstrated in recent dissertations in the field of educational leadership. Power tables provided in Cohen's (1988) Statistical Power Analysis for the Behavioral Sciences were used to determine the power of the statistical tests conducted in dissertations selected from five universities in Tennessee. The meta-analytic approach was used to summarize and synthesize the findings. The population of this study consisted of all dissertations successfully defended by doctoral students majoring in educational leadership/administration at East Tennessee State University, the University of Tennessee at Knoxville, Tennessee State University, the University of Memphis, and Vanderbilt University from January 1, 1996 through December 31, 1998. Dissertations were included if statistical significance testing was used, if the reported tests were referenced in associated power tables from Cohen's (1988) Statistical Power Analysis for the Behavioral Sciences, and if sample sizes were reported in the study. Eighty out of 221 reviewed dissertations were analyzed and statistical power was calculated for each of the 2629 significance tests. The mean statistical power level was calculated for each dissertation. The mean power was .34 to detect small effects, .79 to detect medium effects, and .94 to detect large effects with the dissertation as the unit of analysis. The mean power level across all significance tests was .29 to detect small effects, .75 to detect medium effects, and .93 to detect large effects. These results demonstrated the highest statistical power levels for detecting large and medium effects. The statistical power estimates were quite low when a small effect size was assumed. Researchers had a very low probability of finding true significant differences when looking for small effects. Though the degree of statistical power demonstrated in analyzed dissertations was satisfactory for large and medium effect sizes, neither power level nor Type II error was mentioned in any of the 80 dissertations that were analyzed. Therefore, it is hard to determine whether these dissertations were undertaken with consideration of Type II error or the level of statistical power. The mean sample size used for the 2,629 significance tests was 2.5 times the mean optimal sample size, although most significance tests used samples that were much smaller than optimal sample size. It is recommended that doctoral students in educational leadership receive additional training on the importance of statistical power and the process for estimating appropriate sample size.

Over the past several decades there has been extensive research done in an attempt to determine what demographic characteristics affect economic growth, measured in GDP per capita. Understanding what influences the growth of a country will vastly help policy makers enact policies to lead the country in a positive direction. This research focuses on isolating a new variable, women in the work force. As well as isolating a new variable, this research will modify a preexisting variable that was shown to be significant in order to make the variable more robust and sensitive to recessions. The intent of this thesis is to explore the relationship between several demographic characteristics and their effect on the growth rate of GDP per capita. The first step is to reproduce the work done by Barlow (1994) to ensure that the United States follows similar rules as the countries in his research. Afterwards, we will introduce new variables into the model, comparing the goodness of fit through the methods of R-squared, AIC and BIC. There have been several models developed to answer each of the research questions independently.

<p>This project aims to give an overview of knots, orderability of knot groups, and to construct knots for which the knot groups enjoy some nice properties.</p> <p>To accomplish this, we first present some preliminary results concerning knots and knot groups. We then introduce the Alexander polynomial, and explain the idea of a special polynomial originally introduced by Linnell, Rhemtulla and Rolfsen. By investigating the conditions on a special polynomial, we classify all the special Alexander polynomial of fibred knots of degree less than 10. Finally we construct examples of fibred knots which have a special Alexander polynomial.</p> / Master of Science (MS)