期刊
ELECTRONIC JOURNAL OF STATISTICS
卷 9, 期 2, 页码 2475-2527出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/15-EJS1078
关键词
Credible set; coverage; uncertainty quantification
资金
- Netherlands Organization for Scientific Research (NWO)
- European Research Council under ERC [320637]
We investigate two empirical Bayes methods and a hierarchical Bayes method for adapting the scale of a Gaussian process prior in a nonparametric regression model. We show that all methods lead to a posterior contraction rate that adapts to the smoothness of the true regression function. Furthermore, we show that the corresponding credible sets cover the true regression function whenever this function satisfies a certain extrapolation condition. This condition depends on the specific method, but is implied by a condition of self-similarity. The latter condition is shown to be satisfied with probability one under the prior distribution.
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