Bayesian inverse problems

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

Research output: Book/ReportReportAcademic

80 Citations (Scopus)

Abstract

The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case credible sets are of the correct order of magnitude. The results are numerically illustrated by the problem of recovering a function from observation of a noisy version of its primitive.
Original languageEnglish
Publishers.n.
Publication statusPublished - 2011

Publication series

NamearXiv.org
Volume1103.2692

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  • Cite this

    Knapik, B. T., Vaart, van der, A. W., & Zanten, van, J. H. (2011). Bayesian inverse problems. (arXiv.org; Vol. 1103.2692). s.n.