Title page for ETD etd-121506-145455

Document Type thesis

Author Name Marjerison, William M

Email Address wmarjeri at fastmail.fm

URN etd-121506-145455

Title Bayesian Logistic Regression with Spatial Correlation: An Application to Tennessee River Pollution

Degree MS

Department Mathematical Sciences

Advisors
Balgobin Nandram, Advisor

Keywords
logistic regression
Bayesian statistics
MCMC
spatial statistics

Date of Presentation/Defense 2006-12-15

Availability unrestricted

Abstract
We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic.

In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once.

We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution.

Files
marjerison_thesis.pdf

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Document Type	thesis
Author Name	Marjerison, William M
Email Address	wmarjeri at fastmail.fm
URN	etd-121506-145455
Title	Bayesian Logistic Regression with Spatial Correlation: An Application to Tennessee River Pollution
Degree	MS
Department	Mathematical Sciences
Advisors	Balgobin Nandram, Advisor
Keywords	logistic regression Bayesian statistics MCMC spatial statistics
Date of Presentation/Defense	2006-12-15
Availability	unrestricted
Abstract We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic. In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once. We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution.
Files	marjerison_thesis.pdf