41 research outputs found
Bayesian inference of the initial conditions from large-scale structure surveys
Analysis of three-dimensional cosmological surveys has the potential to
answer outstanding questions on the initial conditions from which structure
appeared, and therefore on the very high energy physics at play in the early
Universe. We report on recently proposed statistical data analysis methods
designed to study the primordial large-scale structure via physical inference
of the initial conditions in a fully Bayesian framework, and applications to
the Sloan Digital Sky Survey data release 7. We illustrate how this approach
led to a detailed characterization of the dynamic cosmic web underlying the
observed galaxy distribution, based on the tidal environment.Comment: 4 pages, 3 figures. Proceedings of IAU Symposium 308 "The Zeldovich
Universe: Genesis and Growth of the Cosmic Web", Tallinn, Estonia, June
23-28, 2014 (eds R. van de Weygaert, S. Shandarin, E. Saar, J. Einasto).
Draws from arXiv:1409.6308. arXiv admin note: substantial text overlap with
arXiv:1410.154
Bayesian optimisation for likelihood-free cosmological inference
Many cosmological models have only a finite number of parameters of interest,
but a very expensive data-generating process and an intractable likelihood
function. We address the problem of performing likelihood-free Bayesian
inference from such black-box simulation-based models, under the constraint of
a very limited simulation budget (typically a few thousand). To do so, we adopt
an approach based on the likelihood of an alternative parametric model.
Conventional approaches to approximate Bayesian computation such as
likelihood-free rejection sampling are impractical for the considered problem,
due to the lack of knowledge about how the parameters affect the discrepancy
between observed and simulated data. As a response, we make use of a strategy
previously developed in the machine learning literature (Bayesian optimisation
for likelihood-free inference, BOLFI), which combines Gaussian process
regression of the discrepancy to build a surrogate surface with Bayesian
optimisation to actively acquire training data. We extend the method by
deriving an acquisition function tailored for the purpose of minimising the
expected uncertainty in the approximate posterior density, in the parametric
approach. The resulting algorithm is applied to the problems of summarising
Gaussian signals and inferring cosmological parameters from the Joint
Lightcurve Analysis supernovae data. We show that the number of required
simulations is reduced by several orders of magnitude, and that the proposed
acquisition function produces more accurate posterior approximations, as
compared to common strategies.Comment: 16+9 pages, 12 figures. Matches PRD published version after minor
modification
Bayesian inference of dark matter voids in galaxy surveys
We apply the BORG algorithm to the Sloan Digital Sky Survey Data Release 7
main sample galaxies. The method results in the physical inference of the
initial density field at a scale factor , evolving gravitationally
to the observed density field at a scale factor , and provides an
accurate quantification of corresponding uncertainties. Building upon these
results, we generate a set of constrained realizations of the present
large-scale dark matter distribution. As a physical illustration, we apply a
void identification algorithm to them. In this fashion, we access voids defined
by the inferred dark matter field, not by galaxies, greatly alleviating the
issues due to the sparsity and bias of tracers. In addition, the use of
full-scale physical density fields yields a drastic reduction of statistical
uncertainty in void catalogs. These new catalogs are enhanced data sets for
cross-correlation with other cosmological probes.Comment: 4 pages, 3 figures. Proceedings of the "49th Rencontres de Moriond"
Cosmology Session, La Thuile, Italy, March 22-29, 2014. Draws from
arXiv:1409.6308 and arXiv:1410.0355. One more figure, updated figures and
references with respect to the published versio
Bayesian large-scale structure inference: initial conditions and the cosmic web
We describe an innovative statistical approach for the ab initio simultaneous
analysis of the formation history and morphology of the large-scale structure
of the inhomogeneous Universe. Our algorithm explores the joint posterior
distribution of the many millions of parameters involved via efficient
Hamiltonian Markov Chain Monte Carlo sampling. We describe its application to
the Sloan Digital Sky Survey data release 7 and an additional non-linear
filtering step. We illustrate the use of our findings for cosmic web analysis:
identification of structures via tidal shear analysis and inference of dark
matter voids.Comment: 4 pages, 3 figures. Proceedings of the IAU Symposium 306 "Statistical
Challenges in 21st Century Cosmology", Lisbon, Portugal, May 25-29, 2014 (eds
A.F. Heavens, J.-L. Starck, A. Krone-Martins). Draws from arXiv:1409.6308 and
arXiv:1410.035
Bayesian large-scale structure inference and cosmic web analysis
Surveys of the cosmic large-scale structure carry opportunities for building
and testing cosmological theories about the origin and evolution of the
Universe. This endeavor requires appropriate data assimilation tools, for
establishing the contact between survey catalogs and models of structure
formation. In this thesis, we present an innovative statistical approach for
the ab initio simultaneous analysis of the formation history and morphology of
the cosmic web: the BORG algorithm infers the primordial density fluctuations
and produces physical reconstructions of the dark matter distribution that
underlies observed galaxies, by assimilating the survey data into a
cosmological structure formation model. The method, based on Bayesian
probability theory, provides accurate means of uncertainty quantification. We
demonstrate the application of BORG to the Sloan Digital Sky Survey data and
describe the primordial and late-time large-scale structure in the observed
volume. We show how the approach has led to the first quantitative inference of
the cosmological initial conditions and of the formation history of the
observed structures. We then use these results for several cosmographic
projects aiming at analyzing and classifying the large-scale structure. In
particular, we build an enhanced catalog of cosmic voids probed at the level of
the dark matter distribution, deeper than with the galaxies. We present
detailed probabilistic maps of the dynamic cosmic web, and offer a general
solution to the problem of classifying structures in the presence of
uncertainty. The results described in this thesis constitute accurate
chrono-cosmography of the inhomogeneous cosmic structure.Comment: 237 pages, 63 figures, 14 tables. PhD thesis, Institut
d'Astrophysique de Paris, September 2015 (advisor: B. Wandelt). Contains the
papers arXiv:1305.4642, arXiv:1409.6308, arXiv:1410.0355, arXiv:1502.02690,
arXiv:1503.00730, arXiv:1507.08664 and draws from arXiv:1403.1260. Full
version including high-resolution figures available from the author's websit
Past and present cosmic structure in the SDSS DR7 main sample
We present a chrono-cosmography project, aiming at the inference of the four
dimensional formation history of the observed large scale structure from its
origin to the present epoch. To do so, we perform a full-scale Bayesian
analysis of the northern galactic cap of the Sloan Digital Sky Survey (SDSS)
Data Release 7 main galaxy sample, relying on a fully probabilistic, physical
model of the non-linearly evolved density field. Besides inferring initial
conditions from observations, our methodology naturally and accurately
reconstructs non-linear features at the present epoch, such as walls and
filaments, corresponding to high-order correlation functions generated by
late-time structure formation. Our inference framework self-consistently
accounts for typical observational systematic and statistical uncertainties
such as noise, survey geometry and selection effects. We further account for
luminosity dependent galaxy biases and automatic noise calibration within a
fully Bayesian approach. As a result, this analysis provides highly-detailed
and accurate reconstructions of the present density field on scales larger than
Mpc, constrained by SDSS observations. This approach also leads to
the first quantitative inference of plausible formation histories of the
dynamic large scale structure underlying the observed galaxy distribution. The
results described in this work constitute the first full Bayesian non-linear
analysis of the cosmic large scale structure with the demonstrated capability
of uncertainty quantification. Some of these results will be made publicly
available along with this work. The level of detail of inferred results and the
high degree of control on observational uncertainties pave the path towards
high precision chrono-cosmography, the subject of simultaneously studying the
dynamics and the morphology of the inhomogeneous Universe.Comment: 27 pages, 9 figure
Comparing cosmic web classifiers using information theory
We introduce a decision scheme for optimally choosing a classifier, which
segments the cosmic web into different structure types (voids, sheets,
filaments, and clusters). Our framework, based on information theory, accounts
for the design aims of different classes of possible applications: (i)
parameter inference, (ii) model selection, and (iii) prediction of new
observations. As an illustration, we use cosmographic maps of web-types in the
Sloan Digital Sky Survey to assess the relative performance of the classifiers
T-web, DIVA and ORIGAMI for: (i) analyzing the morphology of the cosmic web,
(ii) discriminating dark energy models, and (iii) predicting galaxy colors. Our
study substantiates a data-supported connection between cosmic web analysis and
information theory, and paves the path towards principled design of analysis
procedures for the next generation of galaxy surveys. We have made the cosmic
web maps, galaxy catalog, and analysis scripts used in this work publicly
available.Comment: 20 pages, 8 figures, 6 tables. Matches JCAP published version. Public
data available from the first author's website (currently
http://icg.port.ac.uk/~leclercq/