Stat Colloquium: Dr. Jyotishka Datta

Title: Recent Developments in Bayesian Shrinkage for Sparse and Structured Data

Abstract: Sparse signal recovery remains an important challenge in large scale data analysis and global-local (G-L) shrinkage priors have undergone an explosive development in the last decade in both theory and methodology. These developments have established the G-L priors as the state-of-the-art Bayesian tool for sparse signal recovery. In the first part of my talk, I will survey the recent advances in this area, focusing on optimality and performance of G-L priors for both continuous as well as discrete data. In the second part, I will discuss two recent developments, namely, designing a shrinkage prior to handle bi-level sparsity in regression and handling sparse compositional data, routinely observed in microbiomics. I will discuss the methodological challenges associated with each of these problems, and propose to address this gap by using new prior distributions, specially designed to enable handling structured data. I will provide some theoretical support for the proposed methods and show improved performance in simulation settings and application to environmentrics and microbiome data.