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WAVELET SHRINKAGE FOR CORRELATED DATA AND INVERSE PROBLEMS: ADAPTIVITY RESULTS
Adaptation correlated data fractional brownian motion
2015/8/20
Johnstone and Silverman (1997) described a level-dependent thresholding
method for extracting signals from correlated noise. The thresholds were chosen
to minimize a data based unbiased risk criteri...
Bayesian inverse problems with non-conjugate priors
Rate of contraction posterior distribution nonparametric hypothesis testing.
2012/11/23
We investigate the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. A theorem is proved in a gene...
Bayes procedures for adaptive inference in nonparametric inverse problems
Bayes procedures adaptive inference nonparametric inverse problems
2012/11/22
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 ind...
In applications throughout science and engineering one is often faced with the challenge of solving an ill-posed inverse problem, where the number of available measurements is smaller than the dimensi...