Theses/Dissertations - Statistical Sciences
Permanent URI for this collectionhttps://hdl.handle.net/2104/4798
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Browsing Theses/Dissertations - Statistical Sciences by Subject "Bayesian methods."
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Item Bayesian models for discrete censored sampling and dose finding.(2010-06-23T12:29:00Z) Pruszynski, Jessica E.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.We first consider the problem of discrete censored sampling. Censored binomial data may lead to irregular likelihood functions and problems with statistical inference. We consider a Bayesian approach to inference for censored binomial problems and compare it to non-Bayesian methods. We include examples and a simulation study in which we compare point estimation, interval coverage, and interval width for Bayesian and non-Bayesian methods. The continual reassessment method (CRM) is a Bayesian design often used in Phase I cancer clinical trials. It models the toxicity response of the patient as a function of administered dose using a model that is updated as data accrues. The CRM does not take into consideration the relationship between the toxicity response and the proportion of the administered drug that is absorbed by targeted tissue. Not accounting for this discrepancy can yield misleading conclusions about the maximum tolerated dose to be used in subsequent Phase II trials. We will examine, through simulation, the effect that disregarding the level of bioavailability has on the performance of the CRM.Item Count regression models with a misclassified binary covariate : a Bayesian approach.(2010-06-23T12:28:43Z) Morgan-Cox, MaryAnn.; Stamey, James D.; Seaman, John Weldon, 1956-; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Mismeasurment, and specifically misclassification, are inevitable in a variety of regression applications. Fallible measurement methods are often used when infallible methods are either expensive or not available. Ignoring mismeasurement will result in biased estimates for the associated regression parameters. The models presented in this dissertation are designed to correct this bias and yield variance estimates reflecting the uncertainty that is introduced by flawed measurements. We consider a generalized linear model for a Poisson response. This model accounts for the misclassification associated with the binary exposure covariate. In the first portion of the analysis, diffuse priors are utilized for the regression coefficients and the effective prior sample size technique is implemented to construct informative priors for the misclassification parameters. In the second portion of the analysis we place informative priors on the regression parameters and diffuse priors on the misclassification parameters. We also present results of a simulation study that incorporates prior information for both the regression coefficients and the misclassification parameters. Next, we extend the Poisson model with a single binary covariate in various ways, including adding a continuous covariate and accounting for clustering through the use of random effects models. We also consider a zero-inflated version of the model. Simulation studies are summarized for each extension. Finally, we discuss an application in which frequentist and Bayesian logistic regression models are used to predict prevalence of high BMI-for-age among preschool-aged children in Texas.Item Spatial Poisson regression : Bayesian approach correcting for measurement error with applications.(2010-10-08T16:13:31Z) Atkinson, William H., 1980-; Bratcher, Thomas L.; Statistical Sciences.; Baylor University. Dept. of Statistical Sciences.Under and over reporting is a common problem in social science research, adverse events associated with drug use, and many other areas of research. Furthermore, overdispersion is another common problem that plagues count data. McBride (2006) proposed a Bayesian Poisson regression model which accounts for overdispersion in count data. We extend this model by adding parameters to accommodate the problems associated with under and over reporting in the count data. We then study the model's coverage, power, accuracy of point estimates, and credible set widths through simulation using a spatial lattice grid. We find that our proposed model produces reliable point estimates and reasonable credible set widths, coverage, and power. We also provide two examples of the models use: disease mapping of habitat burglary from the city of Waco Texas and an analysis of sports data similar to that of Albert's (1992) analysis of homerun data. Research questions of interest are answered using the subset selection procedure proposed by Bratcher and Bhalla (1974), used by Hamilton, Bratcher, and Stamey (2008) and Stamey, Bratcher, and Young (2007), to demonstrate the ease of use for combining the our model developed here and the subset selection procedure itself, as was also done in McBride (2006).