Physical Sciences and Mathematics Commons^™

Model-Based Imputation Of Below Detection Limit Missing Data And Group Selection In Bayesian Group Index Regression, Matthew Carli

Theses and Dissertations

Investigations into the association between chemical exposure and health outcomes are increasingly focused on the role of chemical mixtures, as opposed to individual chemicals. The analysis of chemical mixture data required the development of novel statistical methods, one of these being Bayesian group index regression. A statistical challenge common to all chemical mixture analyses is the ubiquitous presence of below detection limit (BDL) data. We propose an extension of Bayesian group index regression that treats both regression effects and missing BDL observations as parameters in a model estimated through a Markov Chain Monte Carlo algorithm that we refer to as …

Exploring Improvements To The Convergence Of Reconstructing Historical Destructive Earthquakes, Kameron Lightheart

Theses and Dissertations

Determining risk to human populations due to natural disasters has been a topic of interest in the STEM fields for centuries. Earthquakes and the tsunamis they cause are of particular interest due to their repetition cycles. These cycles can last hundreds of years but we have only had modern measuring instruments for the last century or so which makes analysis difficult. In this document, we explore ways to improve upon an existing method for reconstructing earthquakes from historical accounts of tsunamis. This method was designed and implemented by Jared P Whitehead's research group over the last 5 years. The issue …

Bayesian Calibration Of The Icrp Zirconium Biokinetic Model And Use Of Canned Priors For The Evaluation Of Bioassay, Thomas Raymond Labone

Theses and Dissertations

The International Commission on Radiological Protection (ICRP) publishes biokinetic models that relate measurements of radioactive material in the body and excreta (bioassay) to the amount of the material taken into the body (intake). Given the intake and the biokinetic model, radiation dose to organs and tissues can be calculated. The ICRP approximates the biokinetics of radioactive materials in the body with compartmental models expressed mathematically as a system of ordinary differential equations, for which they provide point estimates of the rate constants. Inaccurate estimates of intake and radiation dose can result in cases where the biokinetics of an individual differ …

Bayesian Nonparametric Model For Functional Data Analysis, Tahmidul Islam

Theses and Dissertations

Functional data analysis (FDA) experienced a burst of growth after Ramsay and Silverman published their textbook in 1997. Functional data analysis interests researchers because of the challenges it adds to well-established multivariate analysis. Unlike finite dimensional random vectors, we visualize infinite dimensional random functions; for example, curves, images, brain scans, etc. A vast amount of literature have been dedicated to developing models for functional data. The ideas are mostly based on basis function representations and kernel-based nonparametric methods. In this dissertation, we propose a Bayesian treatment of nonparametric functional data analysis by introducing a Gaussian process (GP) over the space …

Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones

Theses and Dissertations

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a …

Bayesian Zero-Inflated Model For Ordinal Data, Huizhong Yang

Theses and Dissertations

Datasets with a relatively large number of zeros is commonly seen in medical applications. Although models like Zero-inflated Poisson (ZIP) model are proposed for counts data, there is still some issues with ordinal data which have excess zeros. In this paper, we developed a Bayesian approach to accommodate the excess zero in ordinal data. Intellectual disability (ID), also known as mental retardation (MR), is a disability characterized by below-average intelligence or mental ability and a lack of the learning necessary skills for daily life. A person with intellectual disability has intellectual functioning and adaptive behaviors limitations. Intellectual disability is a …

Bayesian Analysis Of Binary Diagnostic Tests And Panel Count Data, Chunling Wang

Theses and Dissertations

This dissertation mainly explores several challenging topics that arise in diagnostic tests and panel count data in the Bayesian framework. Binary diagnostic tests, particularly multiple diagnostic tests with repeated measures and diagnostic procedures with a large number of raters, are studied. For panel count data, most traditional methods only handle panel count data for a single type of recurrent event. In this dissertation, we primarily focus on the case with multiple types of recurrent events.

In Chapter 1, an introduction to the binary diagnostic tests data and panel count data is presented and related literature works are briefly reviewed. To …

Applications Of Dynamic Linear Models To Random Allocation Models, Albert H. Lee Iii

Theses and Dissertations

Although advances in modern computational algorithms have provided researchers the ability to work problems which were once too computationally complex to solve, problems with high computation or large parameter spaces still remain. Problems such as those involving Time Series can be such problems. Chapter 1 looks at the the use of Exponentially Weighted Moving Averages developed by \citep{holt2004forecasting, winters1960forecasting} which were thought to provide sufficient solutions to these Time Series. A discussion is provided which illustrates the shortcomings of the EWMA and how its infinite number of possible starting values provides the modeler with an endless number of possible solutions …

Mle And Bayesian Methods To Analyze Data With Missing Values Below The Limit Of Detection, Xinxin Hu

Theses and Dissertations

As pesticides are widely used in agriculture, more and more people who work at places like farm are exposed to the pesticides. According to enviroment re- searches [Villarejo; 2003; Reigart and Roberts; 1999], being exposed to some kind of pesticides like Organophosphorus (OP) insecticides has significantly effected the health of farmworkers and their family. The actual level of pesticides can be detected with some limitation for now. However, it is hard to detect when the level is below the limit of detection (LOD). Therefore, the goal of our research is to propose several different methods to analyze data …

Site- And Location-Adjusted Approaches To Adaptive Allocation Clinical Trial Designs, Brian S. Di Pace

Theses and Dissertations

Response-Adaptive (RA) designs are used to adaptively allocate patients in clinical trials. These methods have been generalized to include Covariate-Adjusted Response-Adaptive (CARA) designs, which adjust treatment assignments for a set of covariates while maintaining features of the RA designs. Challenges may arise in multi-center trials if differential treatment responses and/or effects among sites exist. We propose Site-Adjusted Response-Adaptive (SARA) approaches to account for inter-center variability in treatment response and/or effectiveness, including either a fixed site effect or both random site and treatment-by-site interaction effects to calculate conditional probabilities. These success probabilities are used to update assignment probabilities for allocating patients …

Bayesian Semiparametric Methods For Analyzing Panel Count Data, Jianhong Wang

Theses and Dissertations

Panel count data commonly arise in epidemiological, social science, medical studies, in which subjects have repeated measurements on the recurrent events of interest at different observation times. Since the subjects are not under continuous monitoring, the exact times of those recurrent events are not observed but the counts of such events within the adjacent observation times are known. Panel count data can be considered as a special type of longitudinal data with a count response variable in the literature. Compared to the frequentist literature, very limited Bayesian approaches have been developed to analyze panel count data. In this dissertation, several …

Robust Latent Ability Estimation Based On Item Response Information And Model Fit, Hotaka Maeda

Theses and Dissertations

Aberrant testing behaviors may result in inaccurate person trait estimation. To counter its effects, a new robust ability estimation procedure called downweighting of aberrant responses estimation (DARE) is developed. This procedure downweights both uninformative items and model-misfitting response patterns. The purpose of this study is to present DARE and to evaluate its performance against other robust methods, including biweight (Mislevy & Bock, 1982) and biweight-MAP (BMAP; Maeda & Zhang, 2017b). The traditional maximum likelihood (MLE) and maximum a-posteriori (MAP) methods are also included as baseline methods. A Monte Carlo simulation is conducted with the design variables being test length, type …

Development And Application Of Bayesian Semiparametric Models For Dependent Data, Junshu Bao

Theses and Dissertations

Dependent data are very common in many research fields, such as medicine (repeated measures), finance (time series), traffic (clustered), etc. Effective control/modeling of the dependency among data can enhance the performance of the models and result in better prediction. In many cases, the correlation itself may be of great interest. In this dissertation, we develop novel Bayesian semi-/nonparametric regression models to analyze data with various dependence structures. In Chapter 2, a Bayesian non- parametric multivariate ordinal regression model is proposed to fit drinking behavior survey data from DWI offenders. The responses are two-dimensional ordinal data, drinking frequency and drinking quantity …

Bayesian Nonparametric Approaches To Multiple Testing, Density Estimation, And Supervised Learning, William Cipolli Iii

Theses and Dissertations

This dissertation presents methods for several applications of Polya tree models. These novel nonparametric approaches to the problems of multiple testing, density estimation and supervised learning provide an alternative to other parametric and nonparametric models. In Chapter 2, the proposed approximate finite Polya tree multiple testing procedure is very successful in correctly classifying the observations with non-zero mean in a computationally efficient manner; this holds even when the non-zero means are simulated from a mean-zero distribution. Further, the model is capable of this for “interestingly different” observations in the cases where that is of interest. Chapter 3 proposes discrete, and …

Trustworthy, Useful Languages For Probabilistic Modeling And Inference, Neil B. Toronto

Theses and Dissertations

The ideals of exact modeling, and of putting off approximations as long as possible, make Bayesian practice both successful and difficult. Languages for modeling probabilistic processes, whose implementations answer questions about them under asserted conditions, promise to ease much of the difficulty. Unfortunately, very few of these languages have mathematical specifications. This makes them difficult to trust: there is no way to distinguish between an implementation error and a feature, and there is no standard by which to prove optimizations correct. Further, because the languages are based on the incomplete theories of probability typically used in Bayesian practice, they place …

Dynamic Bayesian Approaches To The Statistical Calibration Problem, Derick Lorenzo Rivers

Theses and Dissertations

The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used …

Cluster Expansion Models Via Bayesian Compressive Sensing, Lance Jacob Nelson

Theses and Dissertations

The steady march of new technology depends crucially on our ability to discover and design new, advanced materials. Partially due to increases in computing power, computational methods are now having an increased role in this discovery process. Advances in this area speed the discovery and development of advanced materials by guiding experimental work down fruitful paths. Density functional theory (DFT)has proven to be a highly accurate tool for computing material properties. However, due to its computational cost and complexity, DFT is unsuited to performing exhaustive searches over many candidate materials or for extracting thermodynamic information. To perform these types of …

Hierarchical Probit Models For Ordinal Ratings Data, Allison M. Butler

Theses and Dissertations

University students often complete evaluations of their courses and instructors. The evaluation tool typically contains questions about the course and the instructor on an ordinal Likert scale. We assess instructor effectiveness while adjusting for known confounders. We present a probit regression model with a latent variable to measure the instructor effectiveness accounting for student specific covariates, such as student grade in the course, high school and university GPA, and ACT score.

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 …

A Case Study Of Network Design For Middle East Water Distribution, Rachel Bullene

Theses and Dissertations

The Middle Eastern region encompassing Israel, Jordan, and the Palestinian Territories (West Bank and Gaza) is an arid region with fast growing populations. Adequate and equitable access to water for all the people of the region is crucial to the future of Middle East peace. However, the current water distribution system not only fails to provide an adequate and equitable allocation of water, but also results adverse impacts on the environment. This project involves building a mathematical model to aid decision-makers in designing an optimal water distribution network. A new method for incorporating uncertainty in optimization that is based on …

A Bayesian Decision Theoretical Approach To Supervised Learning, Selective Sampling, And Empirical Function Optimization, James Lamond Carroll

Theses and Dissertations

Many have used the principles of statistics and Bayesian decision theory to model specific learning problems. It is less common to see models of the processes of learning in general. One exception is the model of the supervised learning process known as the "Extended Bayesian Formalism" or EBF. This model is descriptive, in that it can describe and compare learning algorithms. Thus the EBF is capable of modeling both effective and ineffective learning algorithms. We extend the EBF to model un-supervised learning, semi-supervised learning, supervised learning, and empirical function optimization. We also generalize the utility model of the EBF to …

Super-Resolution Via Image Recapture And Bayesian Effect Modeling, Neil B. Toronto

Theses and Dissertations

The goal of super-resolution is to increase not only the size of an image, but also its apparent resolution, making the result more plausible to human viewers. Many super-resolution methods do well at modest magnification factors, but even the best suffer from boundary and gradient artifacts at high magnification factors. This thesis presents Bayesian edge inference (BEI), a novel method grounded in Bayesian inference that does not suffer from these artifacts and remains competitive in published objective quality measures. BEI works by modeling the image capture process explicitly, including any downsampling, and modeling a fictional recapture process, which together allow …

An Adaptive Bayesian Approach To Bernoulli-Response Clinical Trials, Andrew W. Stacey

Theses and Dissertations

Traditional clinical trials have been inefficient in their methods of dose finding and dose allocation. In this paper a four-parameter logistic equation is used to model the outcome of Bernoulli-response clinical trials. A Bayesian adaptive design is used to fit the logistic equation to the dose-response curve of Phase II and Phase III clinical trials. Because of inherent restrictions in the logistic model, symmetric candidate densities cannot be used, thereby creating asymmetric jumping rules inside the Markov chain Monte Carlo algorithm. An order restricted Metropolis-Hastings algorithm is implemented to account for these limitations. Modeling clinical trials in a Bayesian framework …

Development Of Informative Priors In Microarray Studies, Kassandra M. Fronczyk

Theses and Dissertations

Microarrays measure the abundance of DNA transcripts for thousands of gene sequences, simultaneously facilitating genomic comparisons across tissue types or disease status. These experiments are used to understand fundamental aspects of growth and development and to explore the underlying genetic causes of many diseases. The data from most microarray studies are found in open-access online databases. Bayesian models are ideal for the analysis of microarray data because of their ability to integrate prior information; however, most current Bayesian analyses use empirical or flat priors. We present a Perl script to build an informative prior by mining online databases for similar …

Graphical And Bayesian Analysis Of Unbalanced Patient Management Data, Emily Stewart Righter

Theses and Dissertations

The International Normalizing Ratio (INR) measures the speed at which blood clots. Healthy people have an INR of about one. Some people are at greater risk of blood clots and their physician prescribes a target INR range, generally 2-3. The farther a patient is above or below their prescribed range, the more dangerous their situation. A variety of point-of-care (POC) devices has been developed to monitor patients. The purpose of this research was to develop innovative graphics to help describe a highly unbalanced dataset and to carry out Bayesian analyses to determine which of five devices best manages patients. An …

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 …