Bayesian analysis of spatial and survival models with applications of computation techniques

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Bayesian analysis of spatial and survival models with applications of computation techniques

Please use this identifier to cite or link to this item: http://hdl.handle.net/10355/15886

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dc.contributor.advisor Sun, Dongchu en_US
dc.contributor.author Liu, Yajun
dc.contributor.other University of Missouri-Columbia. Graduate School. Theses and Dissertations. Dissertations. 2012 Dissertations en_US
dc.date.accessioned 2012-10-29T18:28:06Z
dc.date.available 2012-10-29T18:28:06Z
dc.date.issued 2012
dc.date.submitted 2012 Summer en_US
dc.identifier.other LiuY-072012-D20
dc.identifier.uri http://hdl.handle.net/10355/15886
dc.description Title from PDF of title page (University of Missouri--Columbia, viewed on October 29, 2012). en_US
dc.description The 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.description Dissertation advisor: Dr. Dongchu Sun en_US
dc.description Includes bibliographical references. en_US
dc.description Vita. en_US
dc.description Ph. D. University of Missouri--Columbia 2012. en_US
dc.description Dissertations, Academic -- University of Missouri--Columbia -- Statistics. en_US
dc.description "July 2012" en_US
dc.description.abstract This 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.extent x, 132 pages en_US
dc.language.iso en_US en_US
dc.publisher University of Missouri--Columbia en_US
dc.relation.ispartof 2012 Freely available dissertations (MU) en_US
dc.subject Bayesian statistics en_US
dc.subject spatial analysis en_US
dc.subject ratios-of-uniforms en_US
dc.subject survival analysis en_US
dc.subject spatial confounding en_US
dc.title Bayesian analysis of spatial and survival models with applications of computation techniques en_US
dc.type Thesis en_US
thesis.degree.discipline Statistics en_US
thesis.degree.grantor University of Missouri--Columbia en_US
thesis.degree.name Ph. D. en_US
thesis.degree.level Doctoral en_US


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