Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Preconditioning the prior to overcome saturation in Bayesian inverse
  problems   We study Bayesian inference in statistical linear inverse problems with
Gaussian noise and priors in Hilbert space. We focus our interest on the
posterior contraction rate in the small noise limit. Existing results suffer
from a certain saturation phenomenon, when the data generating element is too
smooth compared to the smoothness inherent in the prior. We show how to
overcome this saturation in an empirical Bayesian framework by using a
non-centered data-dependent prior. The center is obtained from a
preconditioning regularization step, which provides us with additional
information to be used in the Bayesian framework. We use general techniques
known from regularization theory. To highlight the significance of the findings
we provide several examples. In particular, our approach allows to obtain and,
using preconditioning improve after saturation, minimax rates of contraction
established in previous studies. We also establish minimax contraction rates in
cases which have not been considered so far.

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The categories of this paper are: hep-ex
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The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: eess
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: physics