Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


Mathematics and Statistics

Committee Chair(s)

Daniel C. Coster


Adler Cutler


John R. Stevens


Zachariah Grompert


Richard Jenson


Bayesian models for repeated measures data are fitted to three different data an analysis projects. Markov Chain Monte Carlo (MCMC) methodology is applied to each case with Gibbs sampling and / or an adaptive Metropolis-Hastings (MH ) algorithm used to simulate the posterior distribution of parameters. We implement a Bayesian model with different variance-covariance structures to an audit fee data set. Block structures and linear models for variances are used to examine the linear trend and different behaviors before and after regulatory change during year 2004-2005. We proposed a Bayesian hierarchical model with latent teacher effects, to determine whether teacher professional development (PD) utilizing cyber-enabled resources lead to meaningful student learning outcomes measured by 8th grade student end-of-year scores (CRT scores) for students with teachers who underwent PD. Bayesian variable selection methods are applied to select teacher learning instrument variables to predict teacher effects. We fit a Bayesian two-part model with the first-part a multivariate probit model and the second-p art a log-normal regression to a repeated measures health care data set to analyze the relationship between Body Mass Index (BMI) and health care expenditures and the correlation between the probability of expenditures and dollar amount spent given expenditures. Models were fitted to a training set and predictions were made on both the training set and the test set.