Bayesian Adaptive Shrinkage Analysis

• Activity Number: 604
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Xinyi Xu*+ and Di Cao
• Companies: Ohio State University and The Ohio State University
• Keywords: Bayesian hierarchical models ; prior elicitation ; shrinkage estimation

Abstract

This work proposes a class of hierarchical priors for high-dimensional parameter estimation with unknown sparsity level. This class of priors contains some widely-used priors as special cases, including the Berger-Strawderman prior, the Normal-Jeffreys prior and the horseshoe prior. It doesn't make any assumptions on the sparsity pattern of the data. Instead, it allows the data to adaptive select the hyper-parameters in the model and thus to determine the shrinkage degree. Moreover, the computation based on this class of priors is tractable even for massive data sets. We compare the performances of our priors with many benchmark alternatives in the literature through simulation studies, and show that our priors consistently provide superior performances under various true distributions with different spasity levels and different shapes.