Bayesian Multivariate Regression for High-dimensional Longitudinal Data with Heavy-tailed Errors
Term of Award
Doctor of Public Health (Dr.P.H.)
Document Type and Release Option
Dissertation (restricted to Georgia Southern)
Copyright Statement / License for Reuse
This work is licensed under a Creative Commons Attribution 4.0 License.
Department of Biostatistics (COPH)
Committee Member 1
Committee Member 2
High-dimensional data occurs when the number of measurements on subjects or sampling units is far greater than the size of the sample in the study. Similar to the popularity of longitudinal data in various biomedical and public health research, high-dimensional longitudinal data are also on the rise in bioinformatics, genomics, and public health research. These data often exhibit heavy-tailed errors or contain outliers in areas such as genomics, finance and more. Application of the traditional ordinary least squares for high dimensional longitudinal data may fail to produce valid estimates due to identifiability issues and specifically in heavy-tailed situations, as it penalizes large deviations inappropriately. To address these issues, we present a method for variable selection and estimation based on the continuous shrinkage priors for multivariate continuous outcomes with heavy-tailed errors. The proposed method is developed in a Bayesian setting and a Gibbs sampler is derived to efficiently sample from the posterior distribution. We compare the method to standard estimation routines in a series of simulation examples as well as on a data set from a gene expression profiling experiment on T-cell activation.
Panchal, Viral, "Bayesian Multivariate Regression for High-dimensional Longitudinal Data with Heavy-tailed Errors" (2016). Electronic Theses and Dissertations. 1407.