Discussion of “Frequentist coverage of adaptive nonparametric Bayesian credible sets”
Ismaël Castillo · The Annals of Statistics · 2015
VI & VIIFirst I would like to congratulate the three authors for a very nice paper.During a visit to Eindhoven in 2010, Botond Szabó and Harry van Zanten mentioned the first steps of this work to me, which concerned the understanding of certain empirical Bayes procedures in the white noise L 2 -setting.Since then, together with Aad van der Vaart, they have broadened their original goals and have produced an impressive and very interesting series of papers on the subject.The present paper is indeed one aspect of a larger body of work, and we will mention a few connections with these related papers below.The authors start from the signal in white noise model, that after projection in L 2 onto an appropriate basis, typically related to the SVD of the operator K of the inverse problem, is translated into a sequence formulation.They choose a prior distribution that makes coordinates independent:1. Priors for Bayesian credible sets.2. Bayesian credible regions and simulations.