Adaptive Bayesian credible bands in regression with a Gaussian process prior

Suzanne Sniekers and Aad Vaart ()
Additional contact information
Suzanne Sniekers: Leiden University
Aad Vaart: Leiden University

Sankhya A: The Indian Journal of Statistics, 2020, vol. 82, issue 2, No 5, 386-425

Abstract: 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.

Keywords: Credible band; Coverage; Uncertainty quantification; Nonparametric Bayes; 62G15; 62G05; 62G20 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s13171-019-00185-0 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00185-0

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13171

DOI: 10.1007/s13171-019-00185-0

Access Statistics for this article

Sankhya A: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya A: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().