The Bayesian Multivariate Regression for High Dimensional Longitudinal Data with Heavy-Tailed Errors

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High-dimensional longitudinal data, also called “large p small n”, which consists of the situation 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 exhibit heavy-tailed errors in frequent situations such as genomics, finance and more or contain outliers. Application of traditional ordinary least squares method for high dimensional longitudinal data will fail to produce valid estimates due to identifiability issues and specifically in heavy tails situation as it penalizes large deviations inappropriately. To address these issues, we present a method for variable selection and estimation based on the horseshoe prior for multivariate continuous outcomes with heavy-tailed errors. The proposed method is developed in a Bayesian setting and 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.


Eastern North American Region International Biometric Society Annual Conference (ENAR)


Austin, TX