Recent Developments in Bayesian Shrinkage for Sparse and Structured Data
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.
Dr. Jyotishka Datta is an assistant professor of statistics at Virginia Tech. Prior to this, he was an assistant professor in the Department of Mathematical Sciences at the University of Arkansas Fayetteville. He received his Bachelors and Masters degree from Indian Statistical Institute, Kolkata, India. and Ph.D. in 2009 from Purdue University under the supervision of Jayanta K. Ghosh and Michael Yu Zhu. His research interest spans Bayesian methodology and theory for structured high-dimensional data. I have contributed to the area of multiple testing, shrinkage estimation, sparse signal recovery, nonparametric Bayes, bioinformatics, and default Bayes. Recent applications include next-gen sequencing studies, auditory neuroscience, ecology and crime forecasting.