Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian inverse problems with Gaussian priors   The posterior distribution in a nonparametric inverse problem is shown to
contract to the true parameter at a rate that depends on the smoothness of the
parameter, and the smoothness and scale of the prior. Correct combinations of
these characteristics lead to the minimax rate. The frequentist coverage of
credible sets is shown to depend on the combination of prior and true
parameter, with smoother priors leading to zero coverage and rougher priors to
conservative coverage. In the latter case credible sets are of the correct
order of magnitude. The results are numerically illustrated by the problem of
recovering a function from observation of a noisy version of its primitive.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph