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Activity Number: 234 - SBSS Student Travel Award Session 2
Type: Topic Contributed
Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
Sponsor: Section on Bayesian Statistical Science
Abstract #328569 Presentation
Title: The Inverse Gamma-Gamma Pior for Optimal Posterior Contraction and Multiple Hypothesis Testing
Author(s): Ray Bai* and Malay Ghosh
Companies: University of Florida and University of Florida
Keywords: multiple testing; normal means problem; shrinkage estimation; sparsity

We study the well-known problem of estimating a sparse n-dimensional unknown mean vector with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can be expressed as scale-mixture normal densities are popular for obtaining sparse estimates of the mean vector. In this talk, we introduce a new shrinkage prior known as the inverse gamma-gamma (IGG) prior. We show that the posterior distribution contracts around the true vector at (near) minimax rate and that the posterior concentrates at a rate faster than those of the horseshoe and horseshoe+ in the the Kullback-Leibler sense. To classify true signals, we also propose a hypothesis test based on thresholding the posterior mean. Taking the loss function to be the expected number of misclassified tests, we show that our test procedure asymptotically attains the optimal Bayes risk exactly. We illustrate through simulations and data analysis that the IGG has excellent finite sample performance for both estimation and classification.

Authors who are presenting talks have a * after their name.

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