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Adaptive Bayesian credible bands in regression with a Gaussian process prior.

Suzanne Sniekers¹, Aad van der Vaart¹

¹Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands.

Sankhya. Series A. (2008)

|September 1, 2020

Summary

This summary is machine-generated.

Credible bands in Bayesian nonparametrics can quantify uncertainty but may be misleading. This study examines their validity in Gaussian process regression, finding they are sometimes accurate confidence sets and sometimes not.

Keywords:

Coverage Credible band Nonparametric Bayes Uncertainty quantification

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Area of Science:

Bayesian statistics
Nonparametric regression
Gaussian processes

Background:

Credible bands are used in Bayesian analysis to quantify uncertainty in unknown functions.
They are analogous to confidence bands in frequentist statistics.
Their validity as a measure of uncertainty requires careful examination.

Purpose of the Study:

To investigate the validity of credible bands in nonparametric regression models.
To assess their performance when the prior distribution is a Gaussian process.
To determine conditions under which credible bands accurately represent uncertainty.

Main Methods:

Utilized a nonparametric regression model.
Employed Gaussian process priors for the unknown function.
Analyzed the properties of credible bands under these assumptions.

Main Results:

Demonstrated that credible bands can have the correct order of magnitude for many true regression functions.
Showed that credible bands can serve as valid confidence sets in certain scenarios.
Identified specific functions for which credible bands can be misleading.

Conclusions:

Credible bands in Gaussian process nonparametric regression are not universally valid as confidence sets.
Their utility depends on the underlying true regression function.
Researchers must be cautious when interpreting credible bands due to potential misleading results.