B1069
Title: Using log Cauchy priors for modeling sparsity
Authors: Zihan Zhu - University of Arizona (United States)
Xueying Tang - University of Arizona (United States) [presenting]
Abstract: Sparsity is often a desired structure for parameters in high-dimensional statistical problems. Within a Bayesian framework, sparsity is usually induced by spike-and-slab priors or global-local shrinkage priors. The latter choice is often expressed as a scale mixture of normal distributions. It marginally places a polynomial-tailed distribution on the parameter. In general, a heavier-tailed distribution has a better performance in estimating sparse parameters. We consider the log Cauchy priors in the normal mean estimation problem. This class of priors is proper while having a tail order arbitrarily close to one. The resulting posterior mean is a shrinkage estimator, and the posterior contraction rate is sharp minimax. We will also demonstrate these theoretical properties through simulations.
