A0723
Title: Shrinkage on the simplex: A Bayesian framework for quantifying sparsity and dependence in compositional data
Authors: Jyotishka Datta - Virginia Polytechnic Institute and State University (United States) [presenting]
Matthew Heiner - Brigham Young University (United States)
David Dunson - Duke University (United States)
Otso Ovaskainen - University of Helsinki (Finland)
Abstract: Sparse signal recovery remains a central challenge in large-scale data analysis. Over the past decade, global-local shrinkage priors have emerged as the Bayesian gold standard for sparse inference and a wide range of nonlinear problems. Yet, discrete compositional data, routinely encountered in fields like microbiomics, pose unique difficulties: The Dirichlet distribution cannot adapt to arbitrary levels of sparsity in high-dimensional probability vectors. A new shrinkage prior is introduced on the simplex, specifically designed to scale to problems with many categories while flexibly capturing both sparsity and dependence among components. Theoretical properties that guarantee adaptive behavior are presented, an efficient posterior sampling scheme is outlined, and through simulations and an application to microbiome data, it is demonstrated that the approach outperforms both standard Dirichlet models and existing alternatives.
