Bayes procedures for adaptive inference in inverse problems for the white noise model

B.T. Knapik, B.T. Szabó, A.W. van der Vaart, J.H. Zanten

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of prior distributions indexed by a hyperparameter that quantifies regularity. We prove that both methods we consider succeed in automatically selecting this parameter optimally, resulting in optimal convergence rates for truths with Sobolev or analytic “smoothness”, without using knowledge about this regularity. Both methods are illustrated by simulation examples.
Original languageEnglish
JournalProbability Theory and Related Fields
DOIs
Publication statusE-pub ahead of print - 22 Feb 2015

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