Physical Sciences and Mathematics Commons^™

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 …

Marginally Interpretable Models And Multilevel Models For Quantile Regression With Random-Effects, Nahid Sultana Sumi

Theses and Dissertations

The quantile regression model is an active area of statistical research that has received a lot of attention. This complements the most widely used statistical tool, that is, mean regression analysis. Quantile regression analysis It has become more flexible because of its properties that include no assumption on the distribution of the response variable, equivalent to monotone transformations, and robustness to outliers. However, regression analysis offers methodological challenges if the observations are not independent. Cluster, multilevel, and repeated measures (longitudinal data) designs introduce such dependence. The correlation between observations on the same units or clusters should be accounted for to …

Multiple Frailty Model For Spatially Correlated Interval-Censored, Wanfang Zhang

Theses and Dissertations

In this paper, we consider the problem of multiple frailty selection for general interval-censored spatial survival data, which often occurs in clinical trials and epidemiological studies. The general interval-censored data is a mixture of left-, right- and interval-censored data. We propose a Bayesian semiparametric approach based on the Cox proportional hazard model, where monotone splines were used for non-parametrical modeling of the cumulative baseline hazards where the variable selection priors were used for frailty selection. A two-stage data augmentation with Poisson latent variables is developed for efficient computation. The approach is evaluated based a simulation study and illustrated using a …

Association Between The Beta Band Neural Response And The Behavioral Performance In Aphasic And Neurologically Intact Individuals, Yilun Zhang

Theses and Dissertations

The complex motor act of speech requires integrating linguistic and sensorimotor processes. Sensorimotor interaction mainly supports speech production in the form of state feedback control architecture. While speaking, subjects react to perturbations in the pitch of voice auditory feedback by changing their tone in the opposite direction to pitch-shift stimuli to compensate for the perceived pitch shift. Aphasia is a communication impairment affecting patients’ speaking, understanding, reading, and writing. The present study aims to examine the association between brain neural activity and the ability for speech auditory feedback error correction in both post-stroke aphasia and neurologically intact individuals. There are …

Correcting For Measurement Error In The Outcome When Estimating The Distribution Of Time To Pregnancy With The Current Duration Approach, Nicole Nasrallah

Theses and Dissertations

The current duration approach to modeling time-to-pregnancy (TTP) models the length of pregnancy attempt for women that are currently attempting pregnancy. There is a scarcity of studies, let alone TTP studies, that account for measurement error in the outcome. Previously, the benefits of a piecewise constant model with regards to bias in estimates of the survival function with measurement error and the parametric modelling of TTP was shown. In this thesis, correcting for measurement error in the outcome with the current duration approach is explored through piecewise constant models with log-normal measurement error. Five different methods are compared to determine …

Using Concurrent Functional Regression To Reconstruct River Stage Data During Flood Events And Identify Influential Functional Measurements, Ryan Pittman

Theses and Dissertations

On October 4, 2015, the Cedar Creek gage at Congaree National Park stopped reporting stages, and the readings did not resume until approximately two weeks later because of record-breaking rainfall that led to some of the worst flooding in South Carolina history. Our goal is to reconstruct the Cedar Creek stage during this missing two-week window. The Congaree River gage in Congaree National Park remained functioning throughout the October 2015 flood, when the stage reached its maximum recorded crest. The stages from the two gages are directly related during floods as water travels through the local spillways and flood planes …

Regression Methods For Group Testing Data, Michael Stutz

Theses and Dissertations

Group testing is an efficient method of disease screening, whereby individual specimens (e.g., blood, urine, etc.) are pooled together and tested as a whole for the presence of disease. A common goal is to use data arising from these testing protocols to better understand the relationship between disease status and potential risk factors (e.g., age, symptom status, etc.). Numerous statistical methodologies have been developed for this purpose, most of which are built within the framework of a generalized linear model. Recent authors have suggested the inadequacy of such regression methods to capture the true functional relationships when nonlinear effects are …

Accurate And Integrative Detection Of Copy Number Variants With High-Throughput Data, Xizhi Luo

Theses and Dissertations

Copy number variation, as a major source of genetic variation in the human genome, are gains or losses of the DNA segments. Copy number variation has gained considerable interest as it plays important roles in human complex diseases. Therefore, accurate detection of CNVs with data generated by modern genotyping technologies, such as SNP array and whole-exome sequencing (WES), comprises a critical step toward a better understanding of disease etiology. However, current statistical methodologies for CNV detection still face analytical challenges due to numerous genetic and technological factors that may lead to spurious findings. First, existing methods assume the independent observations …

A Comparison Of Spatial Clustering Assessment Methods, Nadeesha Dilhani Vidanapathirana

Theses and Dissertations

Spatial clustering detection methods are widely used in many fields of research including sociology, epidemiology, ecology, and criminology. The objective of this study is to assess the performance of four spatial clustering detection methods: the average nearest neighbor ratio, Ripley’s K function, local Moran’s I and Getis-Ord Gi* statistics. We conduct a simulation study to evaluate the performance of each method for areal data under different types of spatial dependence and three different areal structures; a 20x20 regular grid, United States counties in six states and Canadian forward sortation areas (FSAs) in three provinces. The results shows that the empirical …

Bayesian Methods In Analyzing The Association Of Random Variables, Zichen Ma

Theses and Dissertations

This dissertation focuses on studying the association between random variables or random vectors from the Bayesian perspective. In particular, it consists of two topics: (1) hypothesis testing for the independence among groups of random variables; and (2) modeling the dynamic association between two random variables given covariates.

In Chapter 2, a nonparametric approach for testing independence among groups of continuous random variables is proposed. Gaussian-centered multivariate finite Polya tree priors are used to model the underlying probability distributions. Integrating out the random probability measure, a tractable empirical Bayes factor is derived and used as the test statistic. The Bayes factor …

A Simulation-Based Study Of Location-Shift Models Under Non-Normal Conditions, Ummay Khayrunnesa Anika

Theses and Dissertations

In this study, we compare ordinary least squares (OLS), generalized least squares (GLS), M- and quantile regression (QR) estimators for a continuous response variable under different scenarios by conducting a simulation study. We assess the performance of the estimators in terms of bias, average distance, mean squared error, coverage probability, and ratio of estimated standard error and empirical standard deviation. OLS estimator performs the best when the errors are homoscedastic normal or homoscedastic but skewed (exponential) having no outliers. GLS estimator shows good comparative results to QR when the errors are heteroscedastic normal or heteroscedastic heavy-tailed (t-distributed). The most satisfactory …

Statistical Analysis Of A Joint Stochastic Model For Recurrent Competing Risks, Longitudinal Marker, And Health Status, Lili Tong

Theses and Dissertations

Joint modeling approach has been applied in many applications in biomedical, reliability, and social-economic research. For example, in clinical trials and medical research, different kinds of patient information are gathered over time, such as recurrent competing risk events (e.g., relapses of different types of tumor), longitudinal marker (e.g., tumor size), and health status (e.g., if a patient is dead or not). These data are usually correlated, joint models enable the analysis of these correlated data. This dissertation proposes a class of joint dynamic models for simultaneously modeling the three types of processes: a recurrent competing risk (RCR) process, a health …

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 …