Physical Sciences and Mathematics Commons^™

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 …

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 Models For Repeated Measures Data Using Markov Chain Monte Carlo Methods, Yuanzhi Li

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

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) …

Inference For A Zero-Inflated Conway-Maxwell-Poisson Regression For Clustered Count Data., Hyoyoung Choo-Wosoba

Electronic Theses and Dissertations

This dissertation is directed toward developing a statistical methodology with applications of the Conway-Maxwell-Poisson (CMP) distribution (Conway, R. W., and Maxwell, W. L., 1962) to count data. The count data for this dissertation exhibit three different characteristics: clustering, zero inflation, and dispersion. Clustering suggests that observations within clusters are correlated, and the zero inflation phenomenon occurs when the data exhibit excessive zero counts. Dispersion implies that the mean is greater/smaller than the variance unlike a Poisson distribution. The dissertation starts with an introduction of inference for a zero-inflated clustered count data in the first chapter. Then, it presents novel methodologies …

Bivariate Negative Binomial Hurdle With Random Spatial Effects, Robert Mcnutt

Dissertations

Count data with excess zeros widely occur in ecology, epidemiology, marketing, and many other disciplines. Mixture distributions consisting of a point mass at zero and a separate discrete distribution are often employed in regression models to account for excessive zero observations in the data. While Poisson models are very popular for count data, Negative Binomial models provide greater flexibility due to their ability to account for overdispersion.

This research focuses on developing a method for analyzing bivariate count data with excess zeros collected over a lattice. A bivariate Zero-Inflated Negative Binomial Hurdle (ZINBH) regression model with spatial random effects is …