Rejoinder to discussions of "Frequentist coverage of adaptive nonparametric Bayesian credible sets"

TL;DR

This paper is a rejoinder addressing discussions on the frequentist coverage properties of adaptive nonparametric Bayesian credible sets, clarifying and defending the original findings.

Contribution

It provides a detailed response to critiques of the original work on Bayesian credible sets' coverage in nonparametric settings.

Findings

Clarifies the conditions under which adaptive Bayesian credible sets have correct frequentist coverage

Addresses misconceptions and critiques from discussions of the original paper

Reinforces the validity of the original results in specific nonparametric contexts

Abstract

Rejoinder of "Frequentist coverage of adaptive nonparametric Bayesian credible sets" by Szab\'o, van der Vaart and van Zanten [arXiv:1310.4489v5].