Nonparametric statistical inverse problems

By Laurent Cavalier. 2008

183 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7c3d5dc970f4eff5ca7ad1ab2aa83b8d5c063338

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In Computational Mechanics

In Computer Vision and Pattern Recognition

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Citations in the corpus

Analysis of the Gibbs Sampler for Hierarchical Inverse Problems (2013, background): “Note that ξ, whose covariance function is a Dirac delta function, is not realizable in the basic Hilbert space X (instead X is the corresponding Cameron–Martin space) but can be interpreted in process form as, for example, in [8, 12] in the context of inverse problems.”
Bayesian inverse problems with non-conjugate priors (2012, methodology): “Minimax rates are attained by a number of methods, such as generalized Tikhonov regularization amongst others [3, 7].”
Bayes procedures for adaptive inference in inverse problems for the white noise model (2012, background): “For instance, the lower bound over Sobolev balls of regularity β > 0 is given by n−β/(1+2β+2p) and over certain “analytic balls” the lower bound is of the order n−1/2 log1/2+p n (see [8]).”
Modern regularization methods for inverse problems (2018, background): “range of the forward operator K. 4.3 Stochastic Approaches In addition to the deterministic viewpoint a statistical approach has become popular also in innite-dimensional problems more recently (cf. [41, 42, 107, 238, 188, 220]). In such a setup the data f are considered to be random variables drawn”
Comparing parameter choice methods for regularization of ill-posed problems (2011, methodology): “For some methods, there are stronger results involving oracle inequalities [19, 24, 26, 25], which, for continuous white noise, have the form”
Posterior Contraction Rates for the Bayesian Approach to Linear Ill-Posed Inverse Problems (2012, unknown): “The rates in [16] agree with the minimax rates provided the scaling of the prior is optimally chosen, [5].”
Sharp Oracle Inequalities for Aggregation of Affine Estimators (2011, methodology): “As explained in [15, 12], the model of heteroscedastic regression is well suited for describing inverse problems.”
Bayesian Recovery of the Initial Condition for the Heat Equation (2011, background): “This heat conduction inverse problem has been studied in frequentist literature (see, e.g., Bissantz and Holzmann, 2008; Cavalier, 2008, 2011; Golubev and Khas′minskĭı, 1999; Mair, 1994; Mair and Ruymgaart, 1996) and has also been addressed in Bayesian framework (with additional assumptions on the…”
BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS (2011, methodology): “26 92 v2 [ m at h. ST ] 2 3 Fe b 20 12 The Annals of Statistics 2011, Vol. 39, No. 5, 2626–2657 DOI: 10.1214/11-AOS920 c© Institute of Mathematical Statistics, 2011 BAYESIAN INVERSE PROBLEMS WITH GAUSSIAN PRIORS By B. T. Knapik1, A. W. van der Vaart and J. H. van Zanten”
GLOBAL UNIFORM RISK BOUNDS FOR WAVELET DECONVOLUTION ESTIMATORS (2011, background): “It has been extensively studied: we refer to Carroll and Hall [9], Stefanski [37], Stefanski and Carroll [38], Fan [14, 15], Diggle and Hall [12], Goldenshluger [22], Pensky and Vidakovic [36], Delaigle and Gijbels [11], Hesse and Meister [24], Johnstone et al. [25], Johnstone and Raimondo [26], Bis”
Non-Gaussian statistical inverse problems. Part I: Posterior distributions (2012, background): “A more problem-oriented review of infinite-dimensional Bayesian statistical inverse problems can be found in [120], and reviews of statistically oriented inverse problems can be found in [16, 124].”