Bayesian spatial analysis with application to the Missouri Ozark Forest ecosystem project

Abstract

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Bayesian hierarchical framework brings more flexibility by accounting for variation from different levels and improves the estimation of parameters as well as the prediction. When there are so many zeros in the data that it does not readily fit any standard distributions, the data set is refereed to as "zero-inflated". The first part of this dissertation is "Zero-inflated Bayesian Spatial Models with Repeated Measurements". A Bayesian hierarchical model which deals with the spatially correlated continuous data sets with excess zeros is developed. The inference, including simulating from the posterior distributions, predicting on new locations as well as hypothesis testing on the model parameters, is implemented using Markov Chain Monte Carlo (MCMC) techniques. The methodology is also applied to the herbaceous data in the Missouri Ozark Forest Ecosystem Project. The second part is "Multivariate Zero-inflated Bayesian Spatial Models with Repeated Measurements". The univariate zero-inflated spatial model is generalized to a multivariate model as desired by analyzing the multivariate zero-inflated spatial data. The third part is "Objective Bayesian Analysis of Spatial Data with Repeated Measurements". Several objective priors are derived for a Bayesian spatial model with a nugget effect and repeated measurements. The resulted posterior is shown to be proper and a simulation study is conducted to compare these objective priors in term of frequents properties.