Default Bayesian analysis with global-local shrinkage priors

• 成果类型: Article
• 署名作者: Bhadra, Anindya; Datta, Jyotishka; Polson, Nicholas G.; Willard, Brandon
• 署名单位: Purdue University System; Purdue University; Duke University; University of Chicago
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw041
• 发表日期: 2016
• 页码: 955969
• 关键词: asymptotic properties; nuisance parameters; horseshoe estimator; prior distributions; location parameter; inference; Robustness; regression; mixtures; product

摘要

We provide a framework for assessing the default nature of a prior distribution using the property of regular variation, which we study for global-local shrinkage priors. In particular, we show that the horseshoe priors, originally designed to handle sparsity, are regularly varying and thus are appropriate for default Bayesian analysis. To illustrate our methodology, we discuss four problems of noninformative priors that have been shown to be highly informative for nonlinear functions. In each case, we show that global-local horseshoe priors perform as required. Global-local shrinkage priors can separate a low-dimensional signal from high-dimensional noise even for nonlinear functions.