Empirical Priors and Coverage of Posterior Credible Sets in a Sparse Normal Mean Model

Ryan Martin () and Bo Ning ()
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Ryan Martin: North Carolina State University
Bo Ning: Yale University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 8, 477-498

Abstract: Abstract Bayesian methods provide a natural means for uncertainty quantification, that is, credible sets can be easily obtained from the posterior distribution. But is this uncertainty quantification valid in the sense that the posterior credible sets attain the nominal frequentist coverage probability? This paper investigates the frequentist validity of posterior uncertainty quantification based on a class of empirical priors in the sparse normal mean model. In particular, we show that our marginal posterior credible intervals achieve the nominal frequentist coverage probability under conditions slightly weaker than needed for selection consistency and a Bernstein–von Mises theorem for the full posterior, and numerical investigations suggest that our empirical Bayes method has superior frequentist coverage probability properties compared to other fully Bayes methods.

Keywords: Bayesian inference; Bernstein–von Mises theorem; Concentration rate; High-dimensional model; Uncertainty quantification; Primary 62C12; 62F12; Secondary 62E20 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-019-00189-w

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