Statistics and Probability Commons^™

Development Of Commercial Applications For Recycled Plastics Using Finite Element Analysis, Nanjunda Narasimhamurthy

Theses and Dissertations

This thesis investigates the suitability of thermo-kinetically recycled plastics for use in commercial product applications using finite element analysis and statistics. Different recycled material blends were tested and evaluated for their use in commercial product applications. There are six different blends of thermo-kinetically recycled plastics used for testing and CATIA is used for finite element analysis. The different types of thermo-kinetically recycled plastics blends are: pop bottles made of PolyethyleneTeraphthalate (PET), milk jugs made of High-Density Polyethylene (HDPE), Vinyl seats made of Poly Vinyl Chloride (PVC) and small amount of Polypropylene (PP) and Urethane, electronic scrap made of engineering resins …

Modeling Distributions Of Test Scores With Mixtures Of Beta Distributions, Jingyu Feng

Theses and Dissertations

Test score distributions are used to make important instructional decisions about students. The test scores usually do not follow a normal distribution. In some cases, the scores appear to follow a bimodal distribution that can be modeled with a mixture of beta distributions. This bimodality may be due different levels of students' ability. The purpose of this study was to develop and apply statistical techniques for fitting beta mixtures and detecting bimodality in test score distributions. Maximum likelihood and Bayesian methods were used to estimate the five parameters of the beta mixture distribution for scores in four quizzes in a …

Using Box-Scores To Determine A Position's Contribution To Winning Basketball Games, Garritt L. Page

Theses and Dissertations

Basketball is a sport that has become increasingly popular world-wide. At the professional level it is a game in which each of the five positions has a specific responsibility that requires unique skills. It seems likely that it would be valuable for coaches to know which skills for each position are most conducive to winning. Knowing which skills to develop for each position could help coaches optimize each player's ability by customizing practice to contain drills that develop the most important skills for each position that would in turn improve the team's overall ability. Through the use of Bayesian hierarchical …

Estimating The Discrepancy Between Computer Model Data And Field Data: Modeling Techniques For Deterministic And Stochastic Computer Simulators, Emily Joy Dastrup

Theses and Dissertations

Computer models have become useful research tools in many disciplines. In many cases a researcher has access to data from a computer simulator and from a physical system. This research discusses Bayesian models that allow for the estimation of the discrepancy between the two data sources. We fit two models to data in the field of electrical engineering. Using this data we illustrate ways of modeling both a deterministic and a stochastic simulator when specific parametric assumptions can be made about the discrepancy term.

Performance Of Aic-Selected Spatial Covariance Structures For Fmri Data, David A. Stromberg

Theses and Dissertations

FMRI datasets allow scientists to assess functionality of the brain by measuring the response of blood flow to a stimulus. Since the responses from neighboring locations within the brain are correlated, simple linear models that assume independence of measurements across locations are inadequate. Mixed models can be used to model the spatial correlation between observations, however selecting the correct covariance structure is difficult. Information criteria, such as AIC are often used to choose among covariance structures. Once the covariance structure is selected, significance tests can be used to determine if a region of interest within the brain is significantly active. …

Fit-To-Fight: Waist Vs. Waist/Height Measurements To Determine An Individual's Fitness Level A Study In Statistical Regression And Analysis, Steven J. Swiderski

Theses and Dissertations

Air Force members are to be tested for fitness by measuring their abdominal circumference, counting the number of sit-ups and push-ups they can accomplish, and the time it takes them to run 1 and miles. The abdominal measurement is a "one-size-fits-all" fitness standard. This research determines that a person's waist-to-height ratio is a better measurement than the waist measurement to estimate an individual's fitness level. This research estimates that all of the variables used to proxy fitness (Gender, Age, Height, Waist Circumference, Waist-to-Height Ratio, Push-Ups, and Sit-Ups) are statistically significant and do represent good estimators of physical fitness. This research …

The Navigation Potential Of Signals Of Opportunity-Based Time Difference Of Arrival Measurements, Kenneth A. Fisher

Theses and Dissertations

This research introduces the concept of navigation potential, NP, to quantify the intrinsic ability to navigate using a given signal. NP theory is a new, information theory-like concept that provides a theoretical performance limit on estimating navigation parameters from a received signal that is modeled through a stochastic mapping of the transmitted signal and measurement noise. NP theory is applied to SOP-based TDOA systems in general as well as for the Gaussian case. Furthermore, the NP is found for a received signal consisting of the transmitted signal, multiple delayed and attenuated replicas of the transmitted signal, and measurement noise. Multipath-based …

Determining The Optimum Number Of Increments In Composite Sampling, John Ellis Hathaway

Theses and Dissertations

Composite sampling can be more cost effective than simple random sampling. This paper considers how to determine the optimum number of increments to use in composite sampling. Composite sampling terminology and theory are outlined and a model is developed which accounts for different sources of variation in compositing and data analysis. This model is used to define and understand the process of determining the optimum number of increments that should be used in forming a composite. The blending variance is shown to have a smaller range of possible values than previously reported when estimating the number of increments in a …

Customization Of Discriminant Function Analysis For Prediction Of Solar Flares, Evelyn A. Schumer

Theses and Dissertations

This research is an extension to the research conducted by K. Leka and G. Barnes of the Colorado Research Associates Division, Northwest Research Associates, Inc. in Boulder, Colorado (CORA) in which they found no single photospheric solar parameter they considered could sufficiently identify a flare-producing active region (AR). Their research then explored the possibility a linear combination of parameters used in a multivariable discriminant function (DF) could adequately predict solar activity. The purpose of this research is to extend the DF research conducted by Leka and Barnes by refining the method of statistical discriminant analysis (DA) with the goal of …

Ip Algorithm Applied To Proteomics Data, Christopher Lee Green

Theses and Dissertations

Mass spectrometry has been used extensively in recent years as a valuable tool in the study of proteomics. However, the data thus produced exhibits hyper-dimensionality. Reducing the dimensionality of the data often requires the imposition of many assumptions which can be harmful to subsequent analysis. The IP algorithm is a dimension reduction algorithm, similar in purpose to latent variable analysis. It is based on the principle of maximum entropy and therefore imposes a minimum number of assumptions on the data. Partial Least Squares (PLS) is an algorithm commonly used with proteomics data from mass spectrometry in order to reduce the …

Quantifying Initial Condition And Parametric Uncertainties In A Nonlinear Aeroelastic System With An Efficient Stochastic Algorithm, Daniel R. Millman

Theses and Dissertations

There is a growing interest in understanding how uncertainties in flight conditions and structural parameters affect the character of a limit cycle oscillation (LCO) response, leading to failure of an aeroelastic system. Uncertainty quantification of a stochastic system (parametric uncertainty) with stochastic inputs (initial condition uncertainty) has traditionally been analyzed with Monte Carlo simulations (MCS). Probability density functions (PDF) of the LCO response are obtained from the MCS to estimate the probability of failure. A candidate approach to efficiently estimate the PDF of an LCO response is the stochastic projection method. The objective of this research is to extend the …

Instructing Teachers Of Children With Disabilities Within The Church Of Jesus Christ Of Latter-Day Saints, Katie E. Sampson

Theses and Dissertations

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.

Probabilistic Methodology For Record Linkage Determining Robustness Of Weights, Krista Peine Jensen

Theses and Dissertations

Record linkage is the process that joins separately recorded pieces of information for a particular individual from one or more sources. To facilitate record linkage, a reliable computer based approach is ideal. In genealogical research computerized record linkage is useful in combing information for an individual across multiple censuses.

In creating a computerized method for linking censuse records it needs to be determined if weights calculated from one geographical area, can be used to link records from another geographical area. Research performed by Marcie Francis calculates field weights using census records from 1910 and 1920 for Ascension Parish Louisiana. These …

Hiring Practices For Graphic Designers In Utah County, Utah, Landon T. Densley

Theses and Dissertations

The purpose of this study was to show how hiring standards of evidence for graphic designers in Utah County compared with the national standards of evidence. The four major national standards of evidence for hiring graphic designers, identified by American Institute of Graphic Arts (AIGA) and Goldfarb, in order of importance are portfolio, recommendations, personality, and education. The data from this study revealed that Utah County employer's standards of evidence matched up closely to national standards of evidence, but the order of importance was slightly different because personality was ranked ahead of recommendations and education.

Performance Of The Kenward-Project When The Covariance Structure Is Selected Using Aic And Bic, Elisa Valderas Gomez

Theses and Dissertations

Linear mixed models are frequently used to analyze data with random effects and/or repeated measures. A common approach to such analyses requires choosing a covariance structure. Information criteria, such as AIC and BIC, are often used by statisticians to help with this task. However, these criteria do not always point to the true covariance structure and therefore the wrong covariance structure is sometimes chosen. Once this step is complete, Wald statistics are used to test fixed effects. Degrees of freedom for these statistics are not known. However, there are approximation methods, such as Kenward and Roger (KR) and Satterthwaite (SW) …

The "Fair" Triathlon: Equating Standard Deviations Using Non-Linear Bayesian Models, Steven Mckay Curtis

Theses and Dissertations

The Ironman triathlon was created in 1978 by combining events with the longest distances for races then contested in Hawaii in swimming, cycling, and running. The Half Ironman triathlon was formed using half the distances of each of the events in the Ironman. The Olympic distance triathlon was created by combining events with the longest distances for races sanctioned by the major federations for swimming, cycling, and running. The relative importance of each event in overall race outcome was not given consideration when determining the distances of each of the races in modern triathlons. Thus, there is a general belief …

Validation Of Criteria Used To Predict Warfarin Dosing Decisions, Nicole Thomas

Theses and Dissertations

People at risk for blood clots are often treated with anticoagulants, warfarin is such an anticoagulant. The dose's effect is measured by comparing the time for blood to clot to a control time called an INR value. Previous anticoagulant studies have addressed agreement between fingerstick (POC) devices and the standard laboratory, however these studies rely on mathematical formulas as criteria for clinical evaluations, i.e. clinical evaluation vs. precision and bias. Fourteen such criteria were found in the literature. There exists little consistency among these criteria for assessing clinical agreement, furthermore whether these methods of assessing agreement are reasonable estimates of …

An Investigation Of The Effects Of Correlation, Autocorrelation, And Sample Size In Classifier Fusion, Nathan J. Leap

Theses and Dissertations

This thesis extends the research found in Storm, Bauer, and Oxley, 2003. Data correlation effects and sample size effects on three classifier fusion techniques and one data fusion technique were investigated. Identification System Operating Characteristic Fusion (Haspert, 2000), the Receiver Operating Characteristic Within Fusion method (Oxley and Bauer, 2002), and a Probabilistic Neural Network were the three classifier fusion techniques; a Generalized Regression Neural Network was the data fusion technique. Correlation was injected into the data set both within a feature set (autocorrelation) and across feature sets for a variety of classification problems, and sample size was varied throughout. Total …

Generalized Residual Multiple Model Adaptive Estimation Of Parameters And States, Charles D. Ormsby

Theses and Dissertations

This dissertation develops a modification to the standard Multiple Model Adaptive Estimator (MMAE) which allows the use of a new "generalized residual" in the hypothesis conditional probability calculation. The generalized residual is a linear combination of traditional Kalman filter residuals and "post-fit" Kalman filter residuals which are calculated after measurement incorporation. This modified MMAE is termed a Generalized Residual Multiple Model Adaptive Estimator (GRMMAE). The dissertation provides a derivation of the hypothesis conditional probability formula which the GRMMAE uses to calculate probabilities that each elemental filter in the GRMMAE contains the correct parameter value. Through appropriate choice of a single …

Transient Analysis And Applications Of Markov Reward Processes, Jeffrey A. Sipe

Theses and Dissertations

In this thesis, the problem of computing the cumulative distribution function (cdf) of the random time required for a system to first reach a specified reward threshold when the rate at which the reward accrues is controlled by a continuous time stochastic process is considered. This random time is a type of first passage time for the cumulative reward process. The major contribution of this work is a simplified, analytical expression for the Laplace-Stieltjes Transform of the cdf in one dimension rather than two. The result is obtained using two techniques: i) by converting an existing partial differential equation to …

Gaussian Mixture Reduction Of Tracking Multiple Maneuvering Targets In Clutter, Jason L. Williams

Theses and Dissertations

The problem of tracking multiple maneuvering targets in clutter naturally leads to a Gaussian mixture representation of the Provability Density Function (PDF) of the target state vector. State-of-the-art Multiple Hypothesis Tracking (MHT) techniques maintain the mean, covariance and probability weight corresponding to each hypothesis, yet they rely on ad hoc merging and pruning rules to control the growth of hypotheses.

Statistical Process Control: An Application In Aircraft Maintenance Management, Bradley A. Beabout

Theses and Dissertations

Maintenance management at the 135th Airlift Wing, Maryland Air National Guard desires a visualization tool for their maintenance performance metrics. Currently they monitor their metrics via an electronic spreadsheet. They desire a tool that presents the performance information in a graphical manner. This thesis effort focuses on the development of a visualization tool utilizing two of the seven tools offered by Statistical Process Control (SPC). This research demonstrates the application of p-charts and Pareto diagrams in the aircraft maintenance arena. P-charts are used for displaying mission capable (MC) rates and flying scheduling effectiveness (FSE) rates. Pareto diagrams are then used …

Normal Mixture Models For Gene Cluster Identification In Two Dimensional Microarray Data, Eric Scott Harvey

Theses and Dissertations

This dissertation focuses on methodology specific to microarray data analyses that organize the data in preliminary steps and proposes a cluster analysis method which improves the interpretability of the cluster results. Cluster analysis of microarray data allows samples with similar gene expression values to be discovered and may serve as a useful diagnostic tool. Since microarray data is inherently noisy, data preprocessing steps including smoothing and filtering are discussed. Comparing the results of different clustering methods is complicated by the arbitrariness of the cluster labels. Methods for re-labeling clusters to assess the agreement between the results of different clustering techniques …

A Comparison Of Coalescent Estimation Software, Kristen Piggott Shepherd

Theses and Dissertations

Coalescent theory is a method often used by population geneticists in order to make inferences about evolutionary parameters. The coalescent is a stochastic model that approximates ancestral relationships among genes. An understanding of the coalescent pattern of a sample of sequences, along with some knowledge of the mutations that have occurred, provides information about the evolutionary forces that have acted on the population. Processes such as migration, recombination, variable population size, or natural selection are the forces that affect the genealogies and lead to genetic variability in a sample. Coalescent theory provides a statistical description of the variability in the …

Theater-Level Stochastic Air-To-Air Engagement Modeling Via Event Occurrence Networks Using Piecewise Polynomial Approximation, David R. Denhard

Theses and Dissertations

This dissertation investigates a stochastic network formulation termed an event occurrence network (EON). EONs are graphical representations of the superposition of several terminating counting processes. An EON arc represents the occurrence of an event from a group of (sequential) events before the occurrence of events from other event groupings. Events between groups occur independently, but events within a group occur sequentially. A set of arcs leaving a node is a set of competing events, which are probabilistically resolved by order relations. An important EON metric is the probability of being at a particular node or set of nodes at time …

Minimum Distance Estimation For Time Series Analysis With Little Data, Hakan Tekin

Theses and Dissertations

Minimum distance estimate is a statistical parameter estimate technique that selects model parameters that minimize a good-of-fit statistic. Minimum distance estimation has been demonstrated better standard approaches, including maximum likelihood estimators and least squares, in estimating statistical distribution parameters with very small data sets. This research applies minimum distance estimation to the task of making time series predictions with very few historical observations. In a Monte Carlo analysis, we test a variety of distance measures and report the results based on many different criteria. Our analysis tests the robustness of the approach by testing its ability to make predictions when …

Comparative Analysis Of Traditional Versus Computer-Based Survey Instrument Response, Albert E. Franke Iv

Theses and Dissertations

The purpose of this study was to determine if survey medium (paper versus computer) affected responses and response rates in Air Force personnel. The study compared responses and response rates from 900 randomly selected Air Force active-duty members using a paper-based survey, a computer-based survey, and a more complex computer-based survey. The first computer-based survey minimized the differences between itself and the paper-based survey to more accurately quantify any bias due solely to the computer medium. The more complex survey served to maximize differences between itself and the other computer-based survey to more accurately quantify any bias due to programmatic …

Computer-Based Methods For Constructing Two-Level Fractional-Factorial Experimental Designs With A Requirement Set, Steven L. Forsythe

Theses and Dissertations

This dissertation developed four methodologies for computer-aided experimental design of two-level fractional factorial designs with requirement sets (DOE/RS). The requirement sets identify all the experimental factors and the appropriate interaction terms to be evaluated in the experiment. Taguchi graphs and similar manual methods provide techniques for solving the DOE/RS problem. Unfortunately, these methods are limited because they become difficult to use as the number of factors or interaction terms exceeds ten. This research showed that the DOE/RS problem belongs to a class of difficult-to-solve problems known as NP-Complete. It is the combinatorial nature of NP-Complete problems that causes them to …

Efficient Simulation Via Validation And Application Of An External Analytical Model, Thomas H. Irish

Theses and Dissertations

This research makes significant contributions towards improving the efficiency of simulation studies using an external analytical model. The foundation for this research is the analytical control variate (ACV) method. The ACV method can produce significant variance reduction, but the resulting point estimate may exhibit bias. A Monte Carlo sampling method for resolving the bias problem is developed and demonstrated through a queueing network example. The method requires knowledge of the parameters and approximate distributions of the random variables used to produce the ACV. Often, some of these parameters or distributions are not known. Both parametric and non-parametric alternatives to the …

A New Sequential Goodness Of Fit Test For The Three-Parameter Gamma Distribution With Known Shape Based On Skewness And Kurtosis, Chil Ho Park

Theses and Dissertations

This research presents a new sequential goodness of fit test for the three-parameter gamma distribution with a known shape. The test is accomplished by employing two new tests, sample skewness and sample kurtosis, sequentially as test statistics. Unlike the typical goodness of fit test, using parameter estimation methods such as maximum likelihood estimation and minimum distance estimation, this test using the two test statistics above does not involve a substantial degree of computational complexity. Large Monte Carlo simulation has been used to determine critical values and overall significance levels for all combinations of the two tests, and to conduct extensive …