Large Scale Bayesian Inference in Cosmology

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Already the last decade has
witnessed unprecedented progress in the collection of cosmological data.
Presently proposed and designed future cosmological probes and surveys permit
us to anticipate the upcoming avalanche of cosmological information during the
next decades.

The increase of valuable observations needs to be accompanied with the development
of efficient and accurate information processing technology in order to analyse
and interpret this data. In particular, cosmography projects, aiming at studying
the origin and inhomogeneous evolution of

the Universe, involve high dimensional inference methods. For example, 3d
cosmological density and velocity field inference requires to explore on the
order of 10^7 or more parameters. Consequently, such projects critically rely
on state-of-the-art information processing techniques

and, nevertheless, are often on the verge of numerical feasibility with present
day computational resources. For this reason, in this talk I will address
 the problem of high dimensional Bayesian inference from cosmological data
sets, subject to a variety of statistical and systematic uncertainties. In
particular, I will focus on the discussion of selected Markov Chain Monte Carlo
techniques, permitting to efficiently solve inference problems with on the
order of 10^7 parameters. Furthermore, these methods will be exemplified in
various cosmological applications, raging from 3d non-linear density and photometric
redshift inference to 4d physical state inference. These techniques permit us
to exploit cosmologically relevant information from

observations to unprecedented detail and hence will significantly contribute to
the era of precision cosmology.