156 research outputs found
Wiener Reconstruction of Large-Scale Structure from Peculiar Velocities
We present an alternative, Bayesian method for large-scale reconstruction
from observed peculiar velocity data. The method stresses a rigorous treatment
of the random errors and it allows extrapolation into poorly sampled regions in
real space or in k-space. A likelihood analysis is used to determine the
fluctuation power spectrum, followed by a Wiener Filter (WF) analysis to obtain
the minimum-variance mean fields of velocity and mass density. Constrained
Realizations (CR) are then used to sample the statistical scatter about the WF
mean field. The WF/CR method is applied as a demonstration to the Mark III data
with 1200 km/s, 900 km/s, and 500 km/s resolutions. The main reconstructed
structures are consistent with those extracted by the POTENT method. A
comparison with the structures in the distribution of IRAS 1.2Jy galaxies
yields a general agreement. The reconstructed velocity field is decomposed into
its divergent and tidal components relative to a cube of +/-8000 km/s centered
on the Local Group. The divergent component is very similar to the velocity
field predicted from the distribution of IRAS galaxies. The tidal component is
dominated by a bulk flow of 194 +/- 32 km/s towards the general direction of
the Shapley concentration, and it also indicates a significant quadrupole.Comment: 28 pages and 8 GIF figures, Latex (aasms4.sty), submitted to ApJ.
Postscript version of the figures can be obtained by anonymous ftp from:
ftp://alf.huji.ac.il/pub/saleem
Percolation Analysis of a Wiener Reconstruction of the IRAS 1.2 Jy Redshift Catalog
We present percolation analyses of Wiener Reconstructions of the IRAS 1.2 Jy
Redshift Survey. There are ten reconstructions of galaxy density fields in real
space spanning the range to , where
, is the present dimensionless density and
is the bias factor. Our method uses the growth of the largest cluster
statistic to characterize the topology of a density field, where Gaussian
randomized versions of the reconstructions are used as standards for analysis.
For the reconstruction volume of radius, Mpc,
percolation analysis reveals a slight `meatball' topology for the real space,
galaxy distribution of the IRAS survey.
cosmology-galaxies:clustering-methods:numericalComment: Revised version accepted for publication in The Astrophysical
Journal, January 10, 1997 issue, Vol.47
Wiener Reconstruction of The Large Scale Structure
The formalism of Wiener filtering is developed here for the purpose of
reconstructing the large scale structure of the universe from noisy, sparse and
incomplete data. The method is based on a linear minimum variance solution,
given data and an assumed \prior model which specifies the covariance matrix of
the field to be reconstructed. While earlier applications of the Wiener filter
have focused on estimation, namely suppressing the noise in the measured
quantities, we extend the method here to perform both prediction and dynamical
reconstruction. The Wiener filter is used to predict the values of unmeasured
quantities, such as the density field in un-sampled regions of space, or to
deconvolve blurred data. The method is developed, within the context of linear
gravitational instability theory, to perform dynamical reconstruction of one
field which is dynamically related to some other observed field. This is the
case, for example, in the reconstruction of the real space galaxy distribution
from its redshift distribution When the field to be reconstructed is a Gaussian
random field, such as the primordial perturbation field predicted by the
canonical model of cosmology, the Wiener filter can be pushed to its fullest
potential. In such a case the Wiener estimator coincides with the Bayesian
estimator designed to maximize the {\it posterior} probability. The Wiener
filter can be also derived by assuming a quadratic regularization function, in
analogy with the `Maximum Entropy' method. The mean field obtained by the
minimal variance solution can be supplemented with constrained realizations of
the Gaussian field toComment: submitted to ApJ, 45 pages, 7 figures, compressed and uuencoded
Postscript file. (zhfl
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
Topology of the Galaxy Distribution
The history and the major results of the study of the topology of the
large-scale structure are briefly reviewed. Two techniques based on percolation
theory and the genus curve are discussed. The preliminary results of the
percolation analysis of the Wiener reconstruction of the IRAS redshift
catalog are reported.Comment: Latex file with figures in postscript format, 8 page
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