Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Posterior contraction for empirical Bayesian approach to inverse
  problems under non-diagonal assumption   We investigate an empirical Bayesian nonparametric approach to a family of
linear inverse problems with Gaussian prior and Gaussian noise. We consider a
class of Gaussian prior probability measures with covariance operator indexed
by a hyperparameter that quantifies regularity. By introducing two auxiliary
problems, we construct an empirical Bayes method and prove that this method can
automatically select the hyperparameter. In addition, we show that this
adaptive Bayes procedure provides optimal contraction rates up to a slowly
varying term and an arbitrarily small constant, without knowledge about the
regularity index. Our method needs not the prior covariance, noise covariance
and forward operator have a common basis in their singular value decomposition,
enlarging the application range compared with the existing results.

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The categories of this paper are: adap-org
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys