Default Bayesian analysis with global-local shrinkage priors

Anindya Bhadra, Jyotishka Datta, Nicholas G. Polson and Brandon Willard

Biometrika, 2016, vol. 103, issue 4, 955-969

Abstract: 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.

Keywords: Default Bayes; Global-local shrinkage; Noninformative prior; Regular variation; Robustness (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (11)

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