Prior-Less Posterior Inference with Double Empirical Bayes

• Activity Number: 400
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: General Methodology
• Author(s): Ryan Martin*
• Companies: University of Illinois at Chicago
• Keywords: Bayes ; empirical Bayes ; high-dimensional ; posterior concentration ; regularization ; sparsity

Abstract

In high-dimensional problems, selecting a good prior can be a serious challenge for Bayesians. In this talk I will present a new kind of empirical Bayes approach that strikes a balance between a greedy centering of the prior on data, and a likelihood-based regularization that prevents the centering from driving the behavior of the posterior. Applications of this general approach to challenging high-dimensional problems, including inference/variable selection in sparse high-dimensional linear models, sparse precision matrix estimation, and adaptive nonparametric estimation will be considered.