Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bayesian reconstruction of the cosmological large-scale structure:
  methodology, inverse algorithms and numerical optimization   We address the inverse problem of cosmic large-scale structure reconstruction
from a Bayesian perspective. For a linear data model, a number of known and
novel reconstruction schemes, which differ in terms of the underlying signal
prior, data likelihood, and numerical inverse extra-regularization schemes are
derived and classified. The Bayesian methodology presented in this paper tries
to unify and extend the following methods: Wiener-filtering, Tikhonov
regularization, Ridge regression, Maximum Entropy, and inverse regularization
techniques. The inverse techniques considered here are the asymptotic
regularization, the Jacobi, Steepest Descent, Newton-Raphson,
Landweber-Fridman, and both linear and non-linear Krylov methods based on
Fletcher-Reeves, Polak-Ribiere, and Hestenes-Stiefel Conjugate Gradients. The
structures of the up-to-date highest-performing algorithms are presented, based
on an operator scheme, which permits one to exploit the power of fast Fourier
transforms. Using such an implementation of the generalized Wiener-filter in
the novel ARGO-software package, the different numerical schemes are
benchmarked with 1-, 2-, and 3-dimensional problems including structured white
and Poissonian noise, data windowing and blurring effects. A novel numerical
Krylov scheme is shown to be superior in terms of performance and fidelity.
These fast inverse methods ultimately will enable the application of sampling
techniques to explore complex joint posterior distributions. We outline how the
space of the dark-matter density field, the peculiar velocity field, and the
power spectrum can jointly be investigated by a Gibbs-sampling process. Such a
method can be applied for the redshift distortions correction of the observed
galaxies and for time-reversal reconstructions of the initial density field.

15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
2
The categories of this paper are: math