Detecting Brain Activation via Bayesian Mixture of Horseshoe Distributions

• Activity Number: 204 - Bayesian Methods for the Analysis of Complex Brain Imaging Data
• Type: Topic-Contributed
• Date/Time: Tuesday, August 10, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Francesco Denti* and Babak Shahbaba and Michele Guindani and Ricardo Azevedo and Sunil P. Gandhi
• Companies: University of California, Irvine and University of California, Irvine and University of California Irvine and University of California, Irvine and University of California, Irvine
• Keywords: Regularization; Horseshoe distribution; Bayesian Mixture Model; Cluster Shrinkage; Dirichlet Process; fMRI data

Abstract

Variable selection is a central topic in supervised learning models. One can perform variable selection in the Bayesian framework by adopting a regularizing prior for the regression coefficients. This choice will shrink towards zero the parameters associated with the irrelevant covariates. Two main types of priors are used to accomplish this goal: the spike-and-slab and the continuous scale mixtures of Gaussians. We propose a discrete mixture of continuous scale mixtures, providing a connection between the two alternatives. We substitute the observation-specific local shrinkage parameters with cluster shrinkage parameters. Our proposal drastically reduces the number of parameters needed in the model and allows sharing information across coefficients of similar magnitude, improving the shrinkage effect. From a practical perspective, we adopt half-Cauchy priors. This choice leads to a cluster-shrinkage version of the Horseshoe prior, henceforth called the Horseshoe Pit (HSP). We then recast the model in a multiple hypothesis testing framework and apply it to a neurological dataset obtained using a novel whole-brain imaging technique.