Botond Szabo (Eindhoven University of Technology)

On frequentist coverage of Bayesian credible sets

Adaptive techniques for nonparametric estimation have been widely stud- ied in the literature and many rate-adaptive results have been provided for a variety of statistical problems. However an adaptive estimator without any knowledge of its uncertainty is rather uninformative, since one knows that the estimator is optimally close to the true function, but has no information about the actual distance.

In the Bayesian framework credible sets can be constructed to quantify the uncertainty in the posterior distribution. Due to the recent developments of Bayesian computational methods constructing credible sets can be easier than constructing confidence sets from frequentist estimators. The frequentist coverage of credible sets describes to what extent credible sets can be viewed as frequentist confidence sets.

We study the frequentist coverage of empirical Bayes credible sets in the inverse Gaussian white noise model. We show that under some shape con- straint on the true function, called the “self-similarity” property, the credible sets have asymptotic frequentist coverage one and their size is rate adaptive.

This is a joint work with Aad van der Vaart and Harry van Zanten.