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

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  • Ryan Martin

    (North Carolina State University)

  • Bo Ning

    (Yale University)

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.

Suggested Citation

  • Ryan Martin & Bo Ning, 2020. "Empirical Priors and Coverage of Posterior Credible Sets in a Sparse Normal Mean Model," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 477-498, August.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00189-w
    DOI: 10.1007/s13171-019-00189-w
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    References listed on IDEAS

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    1. Carlos M. Carvalho & Nicholas G. Polson & James G. Scott, 2010. "The horseshoe estimator for sparse signals," Biometrika, Biometrika Trust, vol. 97(2), pages 465-480.
    2. Nicholas Syring & Ryan Martin, 2019. "Calibrating general posterior credible regions," Biometrika, Biometrika Trust, vol. 106(2), pages 479-486.
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    Cited by:

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