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Adaptive Bayesian credible bands in regression with a Gaussian process prior

Author

Listed:
  • Suzanne Sniekers

    (Leiden University)

  • Aad Vaart

    (Leiden University)

Abstract

A credible band is the set of all functions between a lower and an upper bound that are constructed so that the set has prescribed mass under the posterior distribution. In a Bayesian analysis such a band is used to quantify the remaining uncertainty on the unknown function in a similar manner as a confidence band. We investigate the validity of a credible band in the nonparametric regression model with the prior distribution on the function given by a Gaussian process. We show that there are many true regression functions for which the credible band has the correct order of magnitude to be used as a confidence set. We also exhibit functions for which the credible band is misleading.

Suggested Citation

  • Suzanne Sniekers & Aad Vaart, 2020. "Adaptive Bayesian credible bands in regression with a Gaussian process prior," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 386-425, August.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00185-0
    DOI: 10.1007/s13171-019-00185-0
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    References listed on IDEAS

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    1. Ghosal,Subhashis & van der Vaart,Aad, 2017. "Fundamentals of Nonparametric Bayesian Inference," Cambridge Books, Cambridge University Press, number 9780521878265, January.
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    Cited by:

    1. Dong Yan & Shota Gugushvili & Aad Vaart, 2024. "Bayesian Linear Inverse Problems in Regularity Scales with Discrete Observations," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 228-254, November.

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