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dc.contributor.advisorChakraborty, Sounakeng
dc.contributor.advisorSun, Jianguo, 1961-eng
dc.contributor.authorWang, Zhenyu (Statistician)eng
dc.date.issued2014eng
dc.date.submitted2014 Summereng
dc.description.abstractHigh dimensional data are more common nowadays, because the collection of such data becomes larger and more complex due to the technology advance of the computer science, biology, etc. The analysis of high dimensional data is different from traditional data analysis, and variable selection for high dimensional data becomes very challenging. Structural equation modeling (SEM) analyzes the relationship between manifest variables and latent variables. The structural equation focuses on analyzing the relationship between latent variables. New proposed methods of these topics are discussed in the dissertation. In the first chapter, we review the basic concept of survival analysis, SEM, and current method of variable selection in those two scenarios. We also introduce the available software package for current methods and relevant data set. In the second chapter, we develop a Bayesian kernel machine model with incorporating existing information on pathways and gene networks in the analysis of DNA microarray data. Each pathway is modeled nonparametrically using reproducing kernel Hilbert space. The pathways and the genes are selected via assigning mixture priors on the pathway indicator variable and the gene indicator variable. This approach helped us in flexible modeling of the pathway effects, which can capture both linear and non-linear effect. Moreover, the model can also pinpoint the important pathways and the important active genes within each pathway. We have also developed an efficient Markov Chain Monte Carlo (MCMC) algorithm to fit our model. We used simulations and a real data analysis, [van 't Veer et al., 2002] breast cancer microarray data, to illustrate the proposed method. In the third chapter, we extend the idea of semiparametric structural equation model where the nonlinear functional relationships are approximated using basis expansions [Guo et al., 2012]. Many basis expansion methods, including cubic splines, are known to induce correlations. In this chapter we compare standard Lasso, Fused Lasso aneng
dc.format.extent1 online resource (3 files) : illustrations (some color)eng
dc.identifier.merlinb10791024xeng
dc.identifier.oclc907476253eng
dc.identifier.urihttps://hdl.handle.net/10355/44511
dc.identifier.urihttps://doi.org/10.32469/10355/44511eng
dc.languageEnglisheng
dc.publisher[University of Missouri--Columbia]eng
dc.relation.ispartofcollectionUniversity of Missouri--Columbia. Graduate School. Theses and Dissertationseng
dc.titleBayesian non-linear methods for survival analysis and structural equation modelseng
dc.typeThesiseng
thesis.degree.disciplineStatistics (MU)eng
thesis.degree.grantorUniversity of Missouri--Columbiaeng
thesis.degree.levelDoctoraleng
thesis.degree.namePh. D.eng


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