Physical Sciences and Mathematics Commons^™

Tolerance Intervals In Random-Effects Models, Kakotan Sanogo

Theses and Dissertations

In the pharmaceutical setting, it is often necessary to establish the shelf life of a drug product and sometimes suitable to assess the risk of product failure at the desired expiry period. The current statistical methodology use confidence intervals for the predicted mean to establish the expiry period and prediction intervals for a predicted new assay value or a tolerance interval for a proportion of the population for use in a risk assessment. A major concern is that most methodology treat a homogeneous subpopulation, say batch, either as a fixed effect and therefore uses a fixed-effects regression model (Graybill, 1976) …

Approximations To Continuous Processes In Hierarchical Models, Amanda Cangelosi

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous-time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty ( …

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 …

Applications Of The Bivariate Gamma Distribution In Nutritional Epidemiology And Medical Physics, Jolene Barker

Theses and Dissertations

In this thesis the utility of a bivariate gamma distribution is explored. In the field of nutritional epidemiology a nutrition density transformation is used to reduce collinearity. This phenomenon will be shown to result due to the independent variables following a bivariate gamma model. In the field of radiation oncology paired comparison of variances is often performed. The bivariate gamma model is also appropriate for fitting correlated variances. A method for simulating bivariate gamma random variables is presented. This method is used to generate data from several bivariate gamma models and the asymptotic properties of a test statistic, suggested for …

Application Of Optimization Techniques To Spectrally Modulated, Spectrally Encoded Waveform Design, Todd W. Beard

Theses and Dissertations

A design process is demonstrated for a coexistent scenario containing Spectrally Modulated, Spectrally Encoded (SMSE) and Direct Sequence Spread Spectrum (DSSS) signals. Coexistent SMSE-DSSS designs are addressed under both perfect and imperfect DSSS code tracking conditions using a non-coherent delay-lock loop (DLL). Under both conditions, the number of SMSE subcarriers and subcarrier spacing are the optimization variables of interest. For perfect DLL code tracking conditions, the GA and RSM optimization processes are considered independently with the objective function being end-to-end DSSS bit error rate. A hybrid GA-RSM optimization process is used under more realistic imperfect DLL code tracking conditions. In …

Variable Selection In Competing Risks Using The L1-Penalized Cox Model, Xiangrong Kong

Theses and Dissertations

One situation in survival analysis is that the failure of an individual can happen because of one of multiple distinct causes. Survival data generated in this scenario are commonly referred to as competing risks data. One of the major tasks, when examining survival data, is to assess the dependence of survival time on explanatory variables. In competing risks, as with ordinary univariate survival data, there may be explanatory variables associated with the risks raised from the different causes being studied. The same variable might have different degrees of influence on the risks due to different causes. Given a set of …

Orthodontic Mini-Implant Failure: Assessing The Relationship To Bone Quality Using Qcbct, Joshua Schneider

Loma Linda University Electronic Theses, Dissertations & Projects

The purpose of this study was to evaluate the cortical bone thickness (mm), cortical bone density (HU), and trabecular bone density (HU) of mini-implants sites in both the maxilla and mandible using QCBCT to determine if they had any effect on mini-implant failure rate. Patient characteristics (age, gender, facial type), mini-implant characteristics (date of placement, manufacturer, length, and diameter), and the mini-implant site (region) were also evaluated. One hundred and six mini-implants in 50 consecutive patients with complete patient records, CBCT information, and T1 radiographs were included in the study. Thirty-four of the 106 mini-implants were considered "failures" resulting in …

A Confidence Paradigm For Classification Systems, Nathan J. Leap

Theses and Dissertations

There is no universally accepted methodology to determine how much confidence one should have in a classifier output. This research proposes a framework to determine the level of confidence in an indication from a classifier system where the output is or can be transformed into a posterior probability estimate. This is a theoretical framework that attempts to unite the viewpoints of the classification system developer (or engineer) and the classification system user (or war-fighter). The paradigm is based on the assumptions that the system confidence acts like, or can be modeled as a value and that indication confidence can be …

The Comparative Radiopacity Between Primary And Permanent Teeth, Robert C. Lee

Loma Linda University Electronic Theses, Dissertations & Projects

Purpose: This in vitro study compared the radiopacity between human primary and permanent enamel and dentin. It also compared the radiopacity between human anterior and posterior teeth.

Methods: Extracted primary and permanent teeth were used in this study. One mm enamel and one mm dentin slices were cut from each extracted tooth. Radiographs were taken of each enamel and dentin specimen 1 mm in thickness along with an aluminum step-wedge using procedures specified in International Standards Organization (ISO) 4049:2000. A densitometer was used to measure the Optical Density (OD) of the radiographs of the specimen and the accompanying aluminum step-wedge. …

Cephalometric Analysis Using Magnetic Resonance Imaging, Wade A. Williams

Loma Linda University Electronic Theses, Dissertations & Projects

Purpose: The purpose of this study was to determine if T1-weighted 3D magnetic resonance images performed at 3.0 Tesla could be used to conduct routine orthodontic cephalometric analysis.

Methods: Three cranial imaging methods were compared using sixteen non-growing subjects (10 male and 6 female) who were not claustrophobic, did not have any metallic restorations on the distal of first molars, had no medical implants and the female subjects were not pregnant. Sagittal cranial images were produced by three methods: (1) a digital lateral cephalometric (LC) radiograph (Orthophos XG Plus, Sirona^TM, Bensheim, Germany), (2) a 12-inch FOV cone beam …

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 …

Estimating The Difference Of Percentiles From Two Independent Populations., Romual Eloge Tchouta

Electronic Theses and Dissertations

We first consider confidence intervals for a normal percentile, an exponential percentile and a uniform percentile. Then we develop confidence intervals for a difference of percentiles from two independent normal populations, two independent exponential populations and two independent uniform populations. In our study, we mainly focus on the maximum likelihood to develop our confidence intervals. The efficiency of this method is examined via coverage rates obtained in a simulation study done with the statistical software R.

Modeling The Progression Of Discrete Paired Longitudinal Data., Jonathan Wesley Hicks

Electronic Theses and Dissertations

It is our intention to derive a methodology for which to model discrete paired longitudinal data. Through the use of transition matrices and maximum likelihood estimation techniques by means of software, we develop a way to model the progression of such data. We provide an example by applying this method to the Wisconsin Epidemiological Study of Diabetic Retinopathy data set. The data set is comprised of individuals, all diabetics, who have had their eyes examined for diabetic retinopathy. The eyes are treated as paired data, and we have the results of the examination at the four unequally spaced time points …

Interval Estimation For The Ratio Of Percentiles From Two Independent Populations., Pius Matheka Muindi

Electronic Theses and Dissertations

Percentiles are used everyday in descriptive statistics and data analysis. In real life, many quantities are normally distributed and normal percentiles are often used to describe those quantities. In life sciences, distributions like exponential, uniform, Weibull and many others are used to model rates, claims, pensions etc. The need to compare two or more independent populations can arise in data analysis. The ratio of percentiles is just one of the many ways of comparing populations. This thesis constructs a large sample confidence interval for the ratio of percentiles whose underlying distributions are known. A simulation study is conducted to evaluate …

Analyzing The Effects Of Coupons And Promotion In The Grocery Retail Sector, Milena Hanna Chotard

Masters Theses

Modern scanner technology is pervasive throughout the retailing sector of the economy and is almost universal in the food retail industry. Along with loyalty programs, it has led to the development of massive databases which accurately and proficiently track the purchasing habits of customers. Making use of this information is one of the most important efforts in the management of this sector to further increase profitability.

This thesis explores the application of several statistical techniques to extract specific information from two large databases of customer purchasing behavior at a major US grocery chain. In particular, we first focus on the …

The Association Of Maternal Intention To Breastfeed, Early Skin-To-Skin Mother/Infant Contact, And Exclusive Breastfeeding During The Maternity Hospital Stay, Leslie Mary Bramson

Loma Linda University Electronic Theses, Dissertations & Projects

Breastfeeding is the optimal method to nourish and nurture an infant. Exclusive breastfeeding rates in the United States have reached the goal of Healthy People 2010 that 75% of mother's breastfeed in the immediate postpartum period. Yet, less than 35% of San Bernardino county mothers and 47.7% of Riverside county mothers are exclusively breastfeeding during their maternity hospital stays, with as many as 50% of the infants being weaned from the breast in the first 14 days of life.

This prospective study examined archived data collected by Perinatal Services Network (PSN) of Loma Linda University Medical Center/Children's Hospital for the …

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

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

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.

Statistical Methods For Image Registration And Denoising, Matthew D. Sambora

Theses and Dissertations

This dissertation describes research into image processing techniques that enhance military operational and support activities. The research extends existing work on image registration by introducing a novel method that exploits local correlations to improve the performance of projection-based image registration algorithms. The dissertation also extends the bounds on image registration performance for both projection-based and full-frame image registration algorithms and extends the Barankin bound from the one-dimensional case to the problem of two-dimensional image registration. It is demonstrated that in some instances, the Cramer-Rao lower bound is an overly-optimistic predictor of image registration performance and that under some conditions, the …

Comparison Of Microleakage In Three Sealant Placement Protocols Vs. The Enamel Loc System, Audrey T. Sheu

Loma Linda University Electronic Theses, Dissertations & Projects

PURPOSE: To evaluate sealant microleakage using four different application techniques.

METHODS: The four application techniques evaluated were acid etch only, Adper L-Pop bonding, Optibond bonding, and Enamel Loc One-Step Sealant. Sixty-four extracted third molar teeth were assigned on one of four application techniques (n=16) and Clinpro sealants applied according to the manufacturer's instructions. The teeth were thermocycled for 500 cycles, dyed, and embedded in resin. The samples were then sectioned and evaluated for microleakage on the buccal and lingual surfaces. Statistical methods employed to analyze the data were the Kruskal-Willis rank test and the Mann-Whitney U test.

RESULTS: No significant …

Knowledge, Perceptions, Beliefs And Behaviors Related To The Prevention Of Hypertension Among Black Seventh-Day Adventists Living In London, Maxine A. Newell

Loma Linda University Electronic Theses, Dissertations & Projects

This study was a cross-sectional survey of the hypertension (HTN) knowledge and risk behaviors of Black Seventh-day Adventists (SDA) in London. Recruitment took take place in 17 predominantly Black SDA churches in London. A questionnaire assessed knowledge and lay-beliefs about HTN and perceptions towards HTN using the health belief model (HBM) constructs of susceptibility, severity, benefits, barriers, and self-efficacy. Cohen’s Perceived Stress Scale was incorporated into the questionnaire. Blood pressure, height, weight and waist circumference were and current lifestyles practices were evaluated for the presence of HTN risk factors.

Of the 312 volunteers, ages 25 to 79, 55% were born …

Effect Of Gutta Percha On The Retention Of A Post Using Different Cements, Saeda H. Basta

Loma Linda University Electronic Theses, Dissertations & Projects

This study evaluated the effect of residual gutta percha on the retention strength of prefabricated post cemented with four different cements. Forty intact mandibular single canal canines or premolars were selected for standardized size and quality, endodontically treated, and decoronated to the cementoenamel junction. A post space was prepared to accommodate Para post XP size 4 (Coltene, Whaledent Inc., Cuy Falls, Ohio) to a depth of 8 mm. The Obtura heated gutta percha system was used to inject a very thin line of gutta percha along one lateral wall to the depth of the future post. Forty obturated teeth were …

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 Impact Of Being Born With Cleft And Cleft Reparative Surgery On Overall Health And Speech Outcomes, Khatansuudal Evsanaa

Master's Theses

Orofacial cleft is one of the most common and treatable birth defects in the world. If left untreated, orofacial cleft can impair normal speech development, growth, and could lead to a number of health consequences later in life. The main motivation of the study is to measure the impact of being born with cleft and the cleft reparative surgery on overall speech and health cleft for teenagers in India using difference-in-differences approach along with household fixed effects method. An overall health outcome was measured using height, weight, grip strength and BMI, and the speech acceptability was measured using a “Universal …

Methods For The Analysis Of Developmental Respiration Patterns., Justin Tyler Peyton

Electronic Theses and Dissertations

This thesis looks at the problem of developmental respiration in Sarcophaga crassipalpis Macquart from the biological and instrumental points of view and adapts mathematical and statistical tools in order to analyze the data gathered. The biological motivation and current state of research is given as well as instrumental considerations and problems in the measurement of carbon dioxide production. A wide set of mathematical and statistical tools are used to analyze the time series produced in the laboratory. The objective is to assemble a methodology for the production and analysis of data that can be used in further developmental respiration research.

Small Sample Methods For The Analysis Of Clustered Binary Data, Lawrence J. Cook

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

There are several solutions for analysis of clustered binary data. However, the two most common tools in use today, generalized estimating equations and random effects or mixed models, rely heavily on asymptotic theory. However, in many situations, such as small or sparse samples, asymptotic assumptions may not be met. For this reason we explore the utility of the quadratic exponential model and conditional analysis to estimate the effect size of a trend parameter in small sample and sparse data settings. Further we explore the computational efficiency of two methods for conducting conditional analysis, the network algorithm and Markov chain Monte …

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.

Uncertainty Assessment Of Aircraft Maintenance Times By Using Evidence Theory And Expert Judgment Elicitation, Huseyin Kudak

Engineering Management & Systems Engineering Theses & Dissertations

The goal of this study is to demonstrate the use of the Dempster-Shafer Theory of evidence as a decision aid to predict aircraft maintenance times during wartime operations using expert judgment elicitation. Increased precision in time estimation enables the jet engine aircraft maintenance facility commander to make more accurate decisions for the Air Force's wartime tactical operations allowing the commander to gain a decisive advantage. A questionnaire was designed to elicit judgments from experts in the Aircraft Maintenance Facility (AMF) to investigate maintenance times of the major failure modes (Ignition, Fuel, and Electrical). Results of the expert judgment elicitation were …

Caffeine Model Identification For Vigilance Performance Prediction, Chun-Hui Huang

Mechanical & Aerospace Engineering Theses & Dissertations

The pharmacodynamics and pharmacokinetics of caffeine have been well characterized. In this study, a caffeine dynamic model is developed to describe its pharmacodynamic effects on vigilance performance. Validated biomathematical models developed to address both individual and group fatigue and alertness in a non-laboratory setting represent a tremendous commercial opportunity. First, a test data set with caffeine effects isolated from circadian and homeostatic effects is created. Then a modeling approach for input and output effects is developed and different model structures for the caffeine effects are considered. Observer/Kalman filter Identification (OKID) algorithm is proposed and developed to identify the caffeine model …