Shrinkage on Simplex: Quantifying Sparsity and Dependence in Compositional Data with a Bayesian Framework

• Activity Number: 74 - Invited E-Poster Session I
• Type: Invited
• Date/Time: Sunday, August 7, 2022 : 8:30 PM to 9:25 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jyotishka Datta* and Matthew J. Heiner and David Dunson and Otso Ovaskainen
• Companies: Virginia Tech and Brigham Young University and Duke University and University of Helsinki
• Keywords: Compositional; Bayesian; Shrinkage; High-dimensional; Sparsity; Mixture

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 as well as default non-linear problems. I will discuss extension to discrete data structures including sparse compositional data, routinely observed in microbiomics, starting with the methodological challenges with the Dirichlet distribution as a shrinkage prior for high-dimensional probabilities for its inability to adapt to an arbitrary level of sparsity, and propose to address this gap by using a new prior distribution, specially designed to enable scaling to data with many categories. I will provide some theoretical support for the proposed methods and show improved performance in several simulation settings and application to microbiome data.