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Articles 61 - 90 of 144
Full-Text Articles in Statistics and Probability
A Bayesian Approach To Missile Reliability, Taylor Hardison Redd
A Bayesian Approach To Missile Reliability, Taylor Hardison Redd
Theses and Dissertations
Each year, billions of dollars are spent on missiles and munitions by the United States government. It is therefore vital to have a dependable method to estimate the reliability of these missiles. It is important to take into account the age of the missile, the reliability of different components of the missile, and the impact of different launch phases on missile reliability. Additionally, it is of importance to estimate the missile performance under a variety of test conditions, or modalities. Bayesian logistic regression is utilized to accurately make these estimates. This project presents both previously proposed methods and ways to …
Adaptive Threat Detector Testing Using Bayesian Gaussian Process Models, Bradley Thomas Ferguson
Adaptive Threat Detector Testing Using Bayesian Gaussian Process Models, Bradley Thomas Ferguson
Theses and Dissertations
Detection of biological and chemical threats is an important consideration in the modern national defense policy. Much of the testing and evaluation of threat detection technologies is performed without appropriate uncertainty quantification. This paper proposes an approach to analyzing the effect of threat concentration on the probability of detecting chemical and biological threats. The approach uses a probit semi-parametric formulation between threat concentration level and the probability of instrument detection. It also utilizes a bayesian adaptive design to determine at which threat concentrations the tests should be performed. The approach offers unique advantages, namely, the flexibility to model non-monotone curves …
Variable Selection And Parameter Estimation Using A Continuous And Differentiable Approximation To The L0 Penalty Function, Douglas Nielsen Vanderwerken
Variable Selection And Parameter Estimation Using A Continuous And Differentiable Approximation To The L0 Penalty Function, Douglas Nielsen Vanderwerken
Theses and Dissertations
L0 penalized likelihood procedures like Mallows' Cp, AIC, and BIC directly penalize for the number of variables included in a regression model. This is a straightforward approach to the problem of overfitting, and these methods are now part of every statistician's repertoire. However, these procedures have been shown to sometimes result in unstable parameter estimates as a result on the L0 penalty's discontinuity at zero. One proposed alternative, seamless-L0 (SELO), utilizes a continuous penalty function that mimics L0 and allows for stable estimates. Like other similar methods (e.g. LASSO and SCAD), SELO produces sparse solutions because the penalty function is …
Hierarchical Bayesian Methods For Evaluation Of Traffic Project Efficacy, Andrew Nolan Olsen
Hierarchical Bayesian Methods For Evaluation Of Traffic Project Efficacy, Andrew Nolan Olsen
Theses and Dissertations
A main objective of Departments of Transportation is to improve the safety of the roadways over which they have jurisdiction. Safety projects, such as cable barriers and raised medians, are utilized to reduce both crash frequency and crash severity. The efficacy of these projects must be evaluated in order to use resources in the best way possible. Five models are proposed for the evaluation of traffic projects: (1) a Bayesian Poisson regression model; (2) a hierarchical Poisson regression model building on model (1) by adding hyperpriors; (3) a similar model correcting for overdispersion; (4) a dynamic linear model; and (5) …
Parameter Estimation For The Two-Parameter Weibull Distribution, Mark A. Nielsen
Parameter Estimation For The Two-Parameter Weibull Distribution, Mark A. Nielsen
Theses and Dissertations
The Weibull distribution, an extreme value distribution, is frequently used to model survival, reliability, wind speed, and other data. One reason for this is its flexibility; it can mimic various distributions like the exponential or normal. The two-parameter Weibull has a shape (γ) and scale (β) parameter. Parameter estimation has been an ongoing search to find efficient, unbiased, and minimal variance estimators. Through data analysis and simulation studies, the following three methods of estimation will be discussed and compared: maximum likelihood estimation (MLE), method of moments estimation (MME), and median rank regression (MRR). The analysis of wind speed data from …
Utilizing Universal Probability Of Expression Code (Upc) To Identify Disrupted Pathways In Cancer Samples, Michelle Rachel Withers
Utilizing Universal Probability Of Expression Code (Upc) To Identify Disrupted Pathways In Cancer Samples, Michelle Rachel Withers
Theses and Dissertations
Understanding the role of deregulated biological pathways in cancer samples has the potential to improve cancer treatment, making it more effective by selecting treatments that reverse the biological cause of the cancer. One of the challenges with pathway analysis is identifying a deregulated pathway in a given sample. This project develops the Universal Probability of Expression Code (UPC), a profile of a single deregulated biological path- way, and projects it into a cancer cell to determine if it is present. One of the benefits of this method is that rather than use information from a single over-expressed gene, it pro- …
Assessment Of Acgh Clustering Methodologies, Serena F. Baker
Assessment Of Acgh Clustering Methodologies, Serena F. Baker
Theses and Dissertations
Array comparative genomic hybridization (aCGH) is a technique for identifying duplications and deletions of DNA at specific locations across a genome. Potential objectives of aCGH analysis are the identification of (1) altered regions for a given subject, (2) altered regions across a set of individuals, and (3) clinically relevant clusters of hybridizations. aCGH analysis can be particularly useful when it identifies previously unknown clusters with clinical relevance. This project focuses on the assessment of existing aCGH clustering methodologies. Three methodologies are considered: hierarchical clustering, weighted clustering of called aCGH data, and clustering based on probabilistic recurrent regions of alteration within …
Application Of Convex Methods To Identification Of Fuzzy Subpopulations, Ryan Lee Eliason
Application Of Convex Methods To Identification Of Fuzzy Subpopulations, Ryan Lee Eliason
Theses and Dissertations
In large observational studies, data are often highly multivariate with many discrete and continuous variables measured on each observational unit. One often derives subpopulations to facilitate analysis. Traditional approaches suggest modeling such subpopulations with a compilation of interaction effects. However, when many interaction effects define each subpopulation, it becomes easier to model membership in a subpopulation rather than numerous interactions. In many cases, subjects are not complete members of a subpopulation but rather partial members of multiple subpopulations. Grade of Membership scores preserve the integrity of this partial membership. By generalizing an analytic chemistry concept related to chromatography-mass spectrometry, we …
Parameter Estimation In Linear-Linear Segmented Regression, Erika Lyn Hernandez
Parameter Estimation In Linear-Linear Segmented Regression, Erika Lyn Hernandez
Theses and Dissertations
Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. The bias and mean squared error of the estimators are considered under differing parameter combinations and sample sizes. Parameters estimated in the model are …
Cluster And Classification Analysis Of Fossil Invertebrates Within The Bird Spring Formation, Arrow Canyon, Nevada: Implications For Relative Rise And Fall Of Sea-Level, Scott L. Morris
Theses and Dissertations
Carbonate strata preserve indicators of local marine environments through time. Such indicators often include microfossils that have relatively unique conditions under which they can survive, including light, nutrients, salinity, and especially water temperature. As such, microfossils are environmental proxies. When these microfossils are preserved in the rock record, they constitute key components of depositional facies. Spence et al. (2004, 2007) has proposed several approaches for determining the facies of a given stratigraphic succession based upon these proxies. Cluster analysis can be used to determine microfossil groups that represent specific environmental conditions. Identifying which microfossil groups exist through time can indicate …
Extensions Of Nearest Shrunken Centroid Method For Classification, Tomohiko Funai
Extensions Of Nearest Shrunken Centroid Method For Classification, Tomohiko Funai
Theses and Dissertations
Stylometry assumes that the essence of the individual style of an author can be captured using a number of quantitative criteria, such as the relative frequencies of noncontextual words (e.g., or, the, and, etc.). Several statistical methodologies have been developed for authorship analysis. Jockers et al. (2009) utilize Nearest Shrunken Centroid (NSC) classification, a promising classification methodology in DNA microarray analysis for authorship analysis of the Book of Mormon. Schaalje et al. (2010) develop an extended NSC classification to remedy the problem of a missing author. Dabney (2005) and Koppel et al. (2009) suggest other modifications of NSC. This paper …
Parameter Estimation And Hypothesis Testing For The Truncated Normal Distribution With Applications To Introductory Statistics Grades, James T. Hattaway
Parameter Estimation And Hypothesis Testing For The Truncated Normal Distribution With Applications To Introductory Statistics Grades, James T. Hattaway
Theses and Dissertations
The normal distribution is a commonly seen distribution in nature, education, and business. Data that are mounded or bell shaped are easily found across various fields of study. Although there is high utility with the normal distribution; often the full range can not be observed. The truncated normal distribution accounts for the inability to observe the full range and allows for inferring back to the original population. Depending on the amount of truncation, the truncated normal has several distinct shapes. A simulation study evaluating the performance of the maximum likelihood estimators and method of moment estimators is conducted and a …
An Adaptive Bayesian Approach To Dose-Response Modeling, Thomas J. Leininger
An Adaptive Bayesian Approach To Dose-Response Modeling, Thomas J. Leininger
Theses and Dissertations
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 …
Parameter Estimation For The Lognormal Distribution, Brenda Faith Ginos
Parameter Estimation For The Lognormal Distribution, Brenda Faith Ginos
Theses and Dissertations
The lognormal distribution is useful in modeling continuous random variables which are greater than or equal to zero. Example scenarios in which the lognormal distribution is used include, among many others: in medicine, latent periods of infectious diseases; in environmental science, the distribution of particles, chemicals, and organisms in the environment; in linguistics, the number of letters per word and the number of words per sentence; and in economics, age of marriage, farm size, and income. The lognormal distribution is also useful in modeling data which would be considered normally distributed except for the fact that it may be more …
Estimating The Effect Of Disability On Medicare Expenditures, David Morris Burk
Estimating The Effect Of Disability On Medicare Expenditures, David Morris Burk
Theses and Dissertations
We consider the effect of disability status on Medicare expenditures. Disabled elderly historically have accounted for a significant portion of Medicare expenditures. Recent demographic trends exhibit a decline in the size of this population, causing some observers to predict declines in Medicare expenditures. There are, however, reasons to be suspicious of this rosy forecast. To better understand the effect of disability on Medicare expenditures, we develop and estimate a model using the generalized method of moments technique. We find that newly disabled elderly generally spend more than those who have been disabled for longer periods of time. Also, we find …
Zero-Inflated Censored Regression Models: An Application With Episode Of Care Data, Jonathan P. Prasad
Zero-Inflated Censored Regression Models: An Application With Episode Of Care Data, Jonathan P. Prasad
Theses and Dissertations
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 …
Meta-Analysis Using Bayesian Hierarchical Models In Organizational Behavior, Michael David Ulrich
Meta-Analysis Using Bayesian Hierarchical Models In Organizational Behavior, Michael David Ulrich
Theses and Dissertations
Meta-analysis is a tool used to combine the results from multiple studies into one comprehensive analysis. First developed in the 1970s, meta-analysis is a major statistical method in academic, medical, business, and industrial research. There are three traditional ways in which a meta-analysis is conducted: fixed or random effects, and using an empirical Bayesian approach. Derivations for conducting meta-analysis on correlations in the industrial psychology and organizational behavior (OB) discipline were reviewed by Hunter and Schmidt (2004). In this approach, Hunter and Schmidt propose an empirical Bayesian analysis where the results from previous studies are used as a prior. This …
Modeling Temperature Reduction In Tendons Using Gaussian Processes Within A Dynamic Linear Model, Richard David Wyss
Modeling Temperature Reduction In Tendons Using Gaussian Processes Within A Dynamic Linear Model, Richard David Wyss
Theses and Dissertations
The time it takes an athlete to recover from an injury can be highly influenced by training procedures as well as the medical care and physical therapy received. When an injury occurs to the muscles or tendons of an athlete, it is desirable to cool the muscles and tendons within the body to reduce inflammation, thereby reducing the recovery time. Consequently, finding a method of treatment that is effective in reducing tendon temperatures is beneficial to increasing the speed at which the athlete is able to recover. In this project, Bayesian inference with Gaussian processes will be used to model …
Xprime: A Method Incorporating Expert Prior Information Into Motif Exploration, Rachel Lynn Poulsen
Xprime: A Method Incorporating Expert Prior Information Into Motif Exploration, Rachel Lynn Poulsen
Theses and Dissertations
One of the primary goals of active research in molecular biology is to better understand the process of transcription regulation. An important objective in understanding transcription is identifying transcription factors that directly regulate target genes. Identifying these transcription factors is a key step toward eliminating genetic diseases or disease susceptibilities that are encoded inside deoxyribonucleic acid (DNA). There is much uncertainty and variation associated with transcription factor binding sites, requiring these sites to be represented stochastically. Although typically each transcription factor prefers to bind to a specific DNA word, it can bind to different variations of that DNA word. In …
Measuring Skill Importance In Women's Soccer And Volleyball, Michelle L. Allan
Measuring Skill Importance In Women's Soccer And Volleyball, Michelle L. Allan
Theses and Dissertations
The purpose of this study is to demonstrate how to measure skill importance for two sports: soccer and volleyball. A division I women's soccer team filmed each home game during a competitive season. Every defensive, dribbling, first touch, and passing skill was rated and recorded for each team. It was noted whether each sequence of plays led to a successful shot. A hierarchical Bayesian logistic regression model is implemented to determine how the performance of the skill affects the probability of a successful shot. A division I women's volleyball team rated each skill (serve, pass, set, etc.) and recorded rally …
Characterizing The Statistical Properties And Global Distribution Of Dansgaard-Oeschger Events, Andrea Michelle Thomas
Characterizing The Statistical Properties And Global Distribution Of Dansgaard-Oeschger Events, Andrea Michelle Thomas
Theses and Dissertations
Ice core records from Greenland have shown times of rapid warming during the most recent glacial period, called Dansgaard-Oeschger (D-O) events. D-O events are important to our understanding of both past climate systems and modern climate volatility. In this paper, we present new approaches for statistically evaluating the existence of cyclicity in D-O events and the possible lagged correlation between the Greenland and Antarctica temperature records. Specifically, we consider permutation testing and bootstrapping methodologies for assessing the cyclicity of D-O events and the correlation between the Greenland and Antarctica records. We find that there is not enough evidence to conclude …
Survival Analysis With High-Dimensional Covariates: An Application In Microarray Studies, David Engler, Yi Li
Survival Analysis With High-Dimensional Covariates: An Application In Microarray Studies, David Engler, Yi Li
Faculty Publications
Use of microarray technology often leads to high-dimensional and low-sample size (HDLSS) data settings. A variety of approaches have been proposed for variable selection in this context. However, only a small number of these have been adapted for time-to-event data where censoring is present. Among standard variable selection methods shown both to have good predictive accuracy and to be computationally efficient is the elastic net penalization approach. In this paper, adaptations of the elastic net approach are presented for variable selection both under the Cox proportional hazards model and under an accelerated failure time (AFT) model. Assessment of the two …
Parameter Estimation For The Beta Distribution, Claire Elayne Bangerter Owen
Parameter Estimation For The Beta Distribution, Claire Elayne Bangerter Owen
Theses and Dissertations
The beta distribution is useful in modeling continuous random variables that lie between 0 and 1, such as proportions and percentages. The beta distribution takes on many different shapes and may be described by two shape parameters, alpha and beta, that can be difficult to estimate. Maximum likelihood and method of moments estimation are possible, though method of moments is much more straightforward. We examine both of these methods here, and compare them to three more proposed methods of parameter estimation: 1) a method used in the Program Evaluation and Review Technique (PERT), 2) a modification of the two-sided power …
Generalized Random Walks, Their Trees, And The Transformation Method Of Option Pricing, Thomas Gordon Stewart
Generalized Random Walks, Their Trees, And The Transformation Method Of Option Pricing, Thomas Gordon Stewart
Theses and Dissertations
The random walk is a powerful model. Chemistry, Physics, and Finance are just a few of the disciplines that model with the random walk. It is clear from its varied uses that despite its simplicity, the simple random walk it very flexible. There is one major drawback, however, to the simple random walk and the geometric random walk. The limiting distribution is either normal, lognormal, or a levy process with infinite variance. This thesis introduces an new random walk aimed at overcoming this drawback. Because the simple random walk and the geometric random walk are special cases of the proposed …
Assessing Multivariate Heritability Through Nonparametric Methods, Benjamin Alan Carper
Assessing Multivariate Heritability Through Nonparametric Methods, Benjamin Alan Carper
Theses and Dissertations
The similarities between generations of living subjects are often quantified by heritability. By distinguishing genotypic variation, or variation due to parental pairings, from phenotypic variation, or normal intraspecies variation, the heritability of traits can be estimated. Due to the multivariate nature of many traits, such as size and shape, computation of heritability can be difficult. Also, assessment of the variation of the heritability estimate is extremely difficult. This study uses nonparametric methods, namely the randomization test and the bootstrap, to obtain both a measure of the extremity of the observed heritability and an assessment of the uncertainty.
Ordinal Regression To Evaluate Student Ratings Data, Emily Brooke Bell
Ordinal Regression To Evaluate Student Ratings Data, Emily Brooke Bell
Theses and Dissertations
Student evaluations are the most common and often the only method used to evaluate teachers. In these evaluations, which typically occur at the end of every term, students rate their instructors on criteria accepted as constituting exceptional instruction in addition to an overall assessment. This presentation explores factors that influence student evaluations using the teacher ratings data of Brigham Young University from Fall 2001 to Fall 2006. This project uses ordinal regression to model the probability of an instructor receiving a good, average, or poor rating. Student grade, instructor status, class level, student gender, total enrollment, term, GE class status, …
A Naive, Robust And Stable State Estimate, Todd Gordon Remund
A Naive, Robust And Stable State Estimate, Todd Gordon Remund
Theses and Dissertations
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.
Optimal Interest Rate For A Borrower With Estimated Default And Prepayment Risk, Scott T. Howard
Optimal Interest Rate For A Borrower With Estimated Default And Prepayment Risk, Scott T. Howard
Theses and Dissertations
Today's mortgage industry is constantly changing, with adjustable rate mortgages (ARM), loans originated to the so-called "subprime" market, and volatile interest rates. Amid the changes and controversy, lenders continue to originate loans because the interest paid over the loan lifetime is profitable. Measuring the profitability of those loans, along with return on investment to the lender is assessed using Actuarial Present Value (APV), which incorporates the uncertainty that exists in the mortgage industry today, with many loans defaulting and prepaying. The hazard function, or instantaneous failure rate, is used as a measure of probability of failure to make a payment. …
The Optimal Weighting Of Pre-Election Polling Data, Gregory K. Johnson
The Optimal Weighting Of Pre-Election Polling Data, Gregory K. Johnson
Theses and Dissertations
Pre-election polls are used to test the political landscape and predict election results. The relative weights for the state-level data from the 2006 U.S. senatorial races are considered based on the date on which the polls were conducted. Long- and short-memory weight functions are developed to specify the relative value of historical polling data. An optimal weight function is estimated by minimizing the discrepancy function between estimates from weighted polls and the election outcomes.
Skill Evaluation In Women's Volleyball, Lindsay W. Florence, Gilbert W. Fellingham, Pat R. Vehrs, Nina P. Mortensen
Skill Evaluation In Women's Volleyball, Lindsay W. Florence, Gilbert W. Fellingham, Pat R. Vehrs, Nina P. Mortensen
Faculty Publications
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 on the quality of the previous contact but not explicitly on contacts further removed in the sequence. We represented these sequences in …