Bayes procedures for adaptive inference in nonparametric inverse problems

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

Research output: Book/ReportReportAcademic


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
Number of pages39
Publication statusPublished - 2012

Publication series
Volume1209.3628 [math.ST]

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