Bayes procedures for adaptive inference in inverse problems for the white noise model
By B. Knapik, Botond Szab'o, A. van der Vaart, J. H. Zanten. Probability theory and related fields, 2012
88 citations recorded by the source corpus.
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.
Subfields: Artificial Intelligence, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/21ab52a65da3ef23509ab14e7816f6eefcb51c62
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Kolyan Ray
- Botond Szab'o
- Judith Rousseau
- I. Castillo
- Richard Nickl
- A. van der Vaart
- Subhashis Ghosal
- Stéphanie van der Pas
In Statistics and Probability
- Kolyan Ray
- Judith Rousseau
- Botond Szab'o
- I. Castillo
- Richard Nickl
- A. van der Vaart
- Subhashis Ghosal
- Stéphanie van der Pas
Citations in the corpus
- Asymptotic behaviour of the empirical Bayes posteriors associated to maximum marginal likelihood estimator (2015, methodology): “In the nonparametric setup, the asymptotic behaviour of the MMLE and its associated EB posterior distribution has been studied in the (inverse) white noise model under various families of Gaussian prior processes by [3, 9, 14, 28, 29], in the nonparametric regression problem with smoothing spline pr”
- A Bernstein–von Mises theorem for smooth functionals in semiparametric models (2013, background): “[34] for linear functionals and adaptive priors in white noise inverse problems.”
- Adaptive Bernstein–von Mises theorems in Gaussian white noise (2014, methodology): “where λ is a positive Lebesgue density on (0,∞) satisfying the following assumption (Assumption 1 of [26]).”