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Full-Text Articles in Biostatistics
Bayesian Variable Selection Strategies In Longitudinal Mixture Models And Categorical Regression Problems., Md Nazir Uddin
Bayesian Variable Selection Strategies In Longitudinal Mixture Models And Categorical Regression Problems., Md Nazir Uddin
Electronic Theses and Dissertations
In this work, we seek to develop a variable screening and selection method for Bayesian mixture models with longitudinal data. To develop this method, we consider data from the Health and Retirement Survey (HRS) conducted by University of Michigan. Considering yearly out-of-pocket expenditures as the longitudinal response variable, we consider a Bayesian mixture model with $K$ components. The data consist of a large collection of demographic, financial, and health-related baseline characteristics, and we wish to find a subset of these that impact cluster membership. An initial mixture model without any cluster-level predictors is fit to the data through an MCMC …
Novel Bayesian Methodology In Multivariate Problems., Debamita Kundu
Novel Bayesian Methodology In Multivariate Problems., Debamita Kundu
Electronic Theses and Dissertations
This dissertation involves developing novel Bayesian methodology for multivariate problems. In particular, it focuses on two contexts: shrinkage based variable selection in multivariate regression and simultaneous covariance estimation of multiple groups. Both these projects are centered around fully Bayesian inference schemes based on hierarchical modeling to capture context-specific features of the data and the development of computationally efficient estimation algorithm. Variable selection over a potentially large set of covariates in a linear model is quite popular. In the Bayesian context, common prior choices can lead to a posterior expectation of the regression coefficients that is a sparse (or nearly sparse) …