Mathematical Sciences Department
Statistics Seminar
Speaker: Dr. Zhuanzhuan Ma, University of Texas Rio Grande Valley
Thursday, November 16, 2023
11:00am - 12:00pm
Zoom Link: https://wpi.zoom.us/j/99064789615
Zoom ID: 99064789615
Title: Sparse Bayesian Variable Selection in High Dimensional Regression
Abstract: With the rapid development of computational technology, Bayesian methods have received much attention in the model selection for high-dimensional data, which are frequently collected in various research and industrial areas. This presentation consists of two distinct but related research projects. In the first project, we construct a Bayesian hierarchical modeling framework for the problems of variable selection in logistic regression of highdimensional settings, in which the model dimension exceeds the sample size. We assign a modified global-local shrinkage prior including horseshoe and normal-gamma priors on the regression coefficients and propose an efficient sampling algorithm based on the Gibbs sampler to draw samples from the full conditional posterior distributions to make the posterior inference. Simulation studies and two real data applications are conducted to compare the performance of the proposed Bayesian method and existing ones in the literature. Given the potential ability of the proposed Bayesian method to be extended to other situations, in the second project, we actively investigate how to generalize our computational framework for parameter estimation and variable selection in Bayesian binary quantile regression. Generalizing this method for high dimensional multi-response problems (e.g., quantitative and qualitative responses) will be an area of future investigation.