期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2019
卷号：82
期号：2
页码：386-425
DOI：10.1007/s13171-019-00185-0
出版社：Indian Statistical Institute
摘要：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.
