New Directions in Bayesian Shrinkage for Sparse, Structured Data

Presented by Jyotishka Datta, Assistant Professor, Department of Statistics, Virginia Tech

Wednesday, February 2, 2022
4:00 p.m. ET
Online

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 as well as default non-linear problems. In the first half 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 half, I will discuss several recent developments, including 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.

Speaker Bio

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 from 2016 to 2020. His research interest spans Bayesian methodology and theory for structured high-dimensional data. He has 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.