Title page for ETD etd-02072003-143850


Type of Document Dissertation
Author Boone, Edward L
URN etd-02072003-143850
Title Bayesian Methodology for Missing Data, Model Selection and Hierarchical Spatial Models with Application to Ecological Data.
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Ye, Keying Committee Chair
Anderson-Cook, Christine M. Committee Member
Prins, Samantha C. Bates Committee Member
Smith, Eric P. Committee Member
Terrell, George R. Committee Member
Keywords
  • Ecological Statistics
  • Bayesian Model Averaging
  • Hierarchical Models
  • Missing at Random
Date of Defense 2003-01-31
Availability unrestricted
Abstract
Ecological data is often fraught with many problems such as Missing Data and Spatial Correlation. In this dissertation we use a data set collected by the Ohio EPA as motivation for studying techniques to address these problems. The data set is concerned with the benthic health of Ohio's waterways. A new method for incorporating covariate structure and missing data mechanisms into missing data analysis is considered. This method allows us to detect relationships other popular methods do not allow. We then further extend this method into model selection. In the special case where the unobserved covariates are assumed normally distributed we use the Bayesian Model Averaging method to average the models, select the highest probability model and do variable assessment. Accuracy in calculating the posterior model probabilities using the Laplace approximation and an approximation based on the Bayesian Information Criterion (BIC) are explored. It is shown that the Laplace approximation is superior to the BIC based approximation using simulation. Finally, Hierarchical Spatial Linear Models are considered for the data and we show how to combine analysis which have spatial correlation within and between clusters.

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