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

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
Publishers.n.
Number of pages39
Publication statusPublished - 2012

Publication series

NamearXiv.org
Volume1209.3628 [math.ST]

Fingerprint

Bayes Procedures
Inverse Problem
Regularity
Hierarchical Bayes
Optimal Convergence Rate
Empirical Bayes
Hyperparameters
Ill-posed Problem
Prior distribution
Smoothness
Quantify
Simulation
Truth
Knowledge
Class

Cite this

Knapik, B. T., Szabó, B. T., Vaart, van der, A. W., & Zanten, van, J. H. (2012). Bayes procedures for adaptive inference in nonparametric inverse problems. (arXiv.org; Vol. 1209.3628 [math.ST]). s.n.
Knapik, B.T. ; Szabó, B.T. ; Vaart, van der, A.W. ; Zanten, van, J.H. / Bayes procedures for adaptive inference in nonparametric inverse problems. s.n., 2012. 39 p. (arXiv.org).
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Knapik, BT, Szabó, BT, Vaart, van der, AW & Zanten, van, JH 2012, Bayes procedures for adaptive inference in nonparametric inverse problems. arXiv.org, vol. 1209.3628 [math.ST], s.n.

Bayes procedures for adaptive inference in nonparametric inverse problems. / Knapik, B.T.; Szabó, B.T.; Vaart, van der, A.W.; Zanten, van, J.H.

s.n., 2012. 39 p. (arXiv.org; Vol. 1209.3628 [math.ST]).

Research output: Book/ReportReportAcademic

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Knapik BT, Szabó BT, Vaart, van der AW, Zanten, van JH. Bayes procedures for adaptive inference in nonparametric inverse problems. s.n., 2012. 39 p. (arXiv.org).