Date of Award

2013

Degree Type

Thesis

Degree Name

M.Sc.

Department

Mathematics and Statistics

First Advisor

Hussein, Abdulkadir

Second Advisor

Nkurunziza, Severien

Keywords

Pure sciences, Additive hazard, Bayesian, Markov chain monte carlo, Spatial, Survival

Rights

CC BY-NC-ND 4.0

Abstract

This thesis will be dealing with the problem of Bayesian estimation in additive survival data models accounting for spatial dependencies. We consider the Aalen's additive hazards model in which baseline hazard function, the regression coecients as well as the covariates are all allowed to be time varying processes. We incorporate in this model an extra random vector of frailties accounting for spatial variations among the observations. Consequently, we propose a Bayesian approach to solving the inference problem for such spatial frailty model by assuming piece-wise constant structure on all timevarying functions in the model and hence, imposing appropriately chosen priors on all model parameters. We then employ some versions of MCMC and Gibbs sampling approaches to carry out the inference about the model parameters and apply the resulting algorithm to Prostate cancer diagnosis data for the state of Louisiana, taken from the Surveillance, Epidemiology, and End Results (SEER) databases.

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