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

@article{Knapik2012BayesPF,
  title={Bayes procedures for adaptive inference in inverse problems for the white noise model},
  author={B. Knapik and B. Szab{\'o} and A. W. Vaart and J. H. Zanten},
  journal={Probability Theory and Related Fields},
  year={2012},
  volume={164},
  pages={771-813}
}
  • B. Knapik, B. Szabó, +1 author J. H. Zanten
  • Published 2012
  • Mathematics
  • Probability Theory and Related Fields
  • 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… CONTINUE READING

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