Bayesian Methodology for Missing Data, Model Selection and Hierarchical Spatial Models with Application to Ecological Data

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2003

Author dc:creator

• Boone, Edward L.

Chair dc:contributor.committeechair

• Ye, Keying

Committee members dc:contributor.committeemember

• Anderson-Cook, Christine M.
• Terrell, George R.
• Prins, Samantha C. Bates
• Smith, Eric P.

• Ecological Statistics
• Bayesian Model Averaging
• Hierarchical Models
• Missing at Random

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-02072003-143850

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/26141