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dc.contributor.advisorSun, Dongchuen_US
dc.contributor.authorLiu, Yajun
dc.contributor.otherUniversity of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2012 Dissertationsen_US
dc.date.issued2012
dc.date.submitted2012 Summeren_US
dc.descriptionTitle from PDF of title page (University of Missouri--Columbia, viewed on October 29, 2012).en_US
dc.descriptionThe entire thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file; a non-technical public abstract appears in the public.pdf file.en_US
dc.descriptionDissertation advisor: Dr. Dongchu Sunen_US
dc.descriptionIncludes bibliographical references.en_US
dc.descriptionVita.en_US
dc.descriptionPh. D. University of Missouri--Columbia 2012.en_US
dc.descriptionDissertations, Academic -- University of Missouri--Columbia -- Statistics.en_US
dc.description"July 2012"en_US
dc.description.abstractThis dissertation discusses the methodologies of applying Bayesian hierarchical models to different data with geographical characteristics or with right-censored failure time. A conditional autoregressive (CAR) prior is used for the model to capture spatial effects. Markov chain Monte Carlo (MCMC) methods are used in the sampling. The Ancillary-Sufficient Interweaving Strategy (ASIS) is applied to improve the performance for some parameters. The convergence of some of the parameters improved greatly, but the others do not have very significant improvement. However, the overall performance has improved greatly since it needs much fewer iterations than using regular Gibbs sampling to achieve convergence. For the survival analysis, we propose a generalized linear mixed model with different effects for the hazard rates, and adopte a cure rate model in Chen et al. (1999) for the hazards. A ratio-of-uniforms method is used to get the posterior density of some parameters that can not be simply sampled by common methods. Both the Weibull model and cure rate models are compared. Moreover, for the same data set, competing risks model is considered by incorporating spatial effect to a latent competing risk model from Gelfand et al. (2000). The sampling method mentioned in Berger & Sun (1993) is adapted for efficiency. Finally, spatial confounding occurs when incorporating spatial effects in a regression model. Several estimators of the coefficients are compared for their Mean Squared Errors. The corresponding prediction errors are also discussed.en_US
dc.format.extentx, 132 pagesen_US
dc.identifier.otherLiuY-072012-D20
dc.identifier.urihttp://hdl.handle.net/10355/15886
dc.publisherUniversity of Missouri--Columbiaen_US
dc.relation.ispartof2012 Freely available dissertations (MU)en_US
dc.subjectBayesian statisticsen_US
dc.subjectspatial analysisen_US
dc.subjectratios-of-uniformsen_US
dc.subjectsurvival analysisen_US
dc.subjectspatial confoundingen_US
dc.titleBayesian analysis of spatial and survival models with applications of computation techniquesen_US
dc.typeThesisen_US
thesis.degree.disciplineStatisticsen_US
thesis.degree.disciplineStatisticseng
thesis.degree.grantorUniversity of Missouri--Columbiaen_US
thesis.degree.levelDoctoralen_US
thesis.degree.namePh. D.en_US


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