234 research outputs found
Parameter inference and model comparison using theoretical predictions from noisy simulations
When inferring unknown parameters or comparing different models, data must be
compared to underlying theory. Even if a model has no closed-form solution to
derive summary statistics, it is often still possible to simulate mock data in
order to generate theoretical predictions. For realistic simulations of noisy
data, this is identical to drawing realizations of the data from a likelihood
distribution. Though the estimated summary statistic from simulated data
vectors may be unbiased, the estimator has variance which should be accounted
for. We show how to correct the likelihood in the presence of an estimated
summary statistic by marginalizing over the true summary statistic in the
framework of a Bayesian hierarchical model. For Gaussian likelihoods where the
covariance must also be estimated from simulations, we present an alteration to
the Sellentin-Heavens corrected likelihood. We show that excluding the proposed
correction leads to an incorrect estimate of the Bayesian evidence with JLA
data. The correction is highly relevant for cosmological inference that relies
on simulated data for theory (e.g. weak lensing peak statistics and simulated
power spectra) and can reduce the number of simulations required.Comment: 9 pages, 6 figures, published by MNRAS. Changes: matches published
version, added Bayesian hierarchical interpretation and probabilistic
graphical mode
Cosmology with the Square Kilometre Array
We argue that the Square Kilometre Array has the potential to make both
redshift (HI) surveys and radio continuum surveys that will revolutionize
cosmological studies, provided that it has sufficient instantaneous
field-of-view that these surveys can cover a hemisphere in a timescale ~1 yr.
Adopting this assumption, we focus on two key experiments which will yield
fundamental new measurements in cosmology, characterizing the properties of the
mysterious dark energy which dominates the dynamics of today's Universe.
Experiment I will map out ~10^9 HI galaxies to redshift z~1.5, providing the
premier measurement of the clustering power spectrum of galaxies: accurately
delineating the acoustic oscillations and the `turnover'. Experiment II will
quantify the cosmic shear distortion of ~10^10 radio continuum sources,
determining a precise power spectrum of the dark matter, and its growth as a
function of cosmic epoch. We contrast the performance of the SKA in precision
cosmology with that of other facilities which will, probably or possibly, be
available on a similar timescale. We conclude that data from the SKA will yield
transformational science as the direct result of four key features: (i) the
immense cosmic volumes probed, exceeding future optical redshift surveys by
more than an order of magnitude; (ii) well-controlled systematic effects such
as the narrow `k-space window function' for Experiment I and the
accurately-known `point-spread function' for Experiment II; (iii) the ability
to measure with high precision large-scale modes in the clustering power
spectra, for which nuisance effects such as non-linear structure growth,
peculiar velocities and `galaxy bias' are minimised; and (iv) different
degeneracies between key parameters to those which are inherent in the CMB.Comment: 20 pages, 8 figures. To appear in "Science with the Square Kilometer
Array", eds. C.Carilli and S.Rawlings, New Astronomy Reviews (Elsevier:
Amsterdam
RadioLensfit: Bayesian weak lensing measurement in the visibility domain
Observationally, weak lensing has been served so far by optical surveys due
to the much larger number densities of background galaxies achieved, which is
typically by two to three orders of magnitude compared to radio. However, the
high sensitivity of the new generation of radio telescopes such as the Square
Kilometre Array (SKA) will provide a density of detected galaxies that is
comparable to that found at optical wavelengths, and with significant source
shape measurements to make large area radio surveys competitive for weak
lensing studies. This will lead weak lensing to become one of the primary
science drivers in radio surveys too, with the advantage that they will access
the largest scales in the Universe going beyond optical surveys, like LSST and
Euclid, in terms of redshifts that are probed. RadioLensfit is an adaptation to
radio data of "lensfit", a model-fitting approach for galaxy shear measurement,
originally developed for optical weak lensing surveys. Its key advantage is
working directly in the visibility domain, which is the natural approach to
adopt with radio data, avoiding systematics due to the imaging process. We
present results on galaxy shear measurements, including investigation of
sensitivity to instrumental parameters such as the visibilities gridding size,
based on simulations of individual galaxy visibilities performed by using
SKA1-MID baseline configuration. We get an amplitude of the shear bias in the
method comparable with SKA1 requirements for a population of galaxies with
realistic flux and scalelength distributions estimated from the VLA SWIRE
catalog.Comment: 4 pages, 4 figures, The many facets of extragalactic radio surveys:
towards new scientific challenges, Bologna 20-23, 201
Radio Galaxy Detection in the Visibility Domain
We explore a new Bayesian method of detecting galaxies from radio
interferometric data of the faint sky. Working in the Fourier domain, we fit a
single, parameterised galaxy model to simulated visibility data of star-forming
galaxies. The resulting multimodal posterior distribution is then sampled using
a multimodal nested sampling algorithm such as MultiNest. For each galaxy, we
construct parameter estimates for the position, flux, scale-length and
ellipticities from the posterior samples. We first test our approach on
simulated SKA1-MID visibility data of up to 100 galaxies in the field of view,
considering a typical weak lensing survey regime (SNR ) where 98% of
the input galaxies are detected with no spurious source detections. We then
explore the low SNR regime, finding our approach reliable in galaxy detection
and providing in particular high accuracy in positional estimates down to SNR
. The presented method does not require transformation of visibilities
to the image domain, and requires no prior knowledge of the number of galaxies
in the field of view, thus could become a useful tool for constructing accurate
radio galaxy catalogs in the future.Comment: 11 pages, 11 figures. Accepted for publication in MNRA
Power-spectrum space decomposition of frequency tomographic data for intensity mapping experiments
We present a Bayesian framework to establish a power-spectrum space
decomposition of frequency tomographic (PSDFT) data for future intensity
mapping (IM) experiments. Different from most traditional component-separation
methods which work in the map domain, this new technique treats multifrequency
power spectra as raw data and can reconstruct component power spectra by taking
advantage of distinct components' correlation patterns in the frequency domain.
We have validated this new technique for both interferometric and
single-dish-like IM experiments, respectively, using synthesized mock data that
contain bright foreground contaminants, IM signals, and instrumental effects at
different frequencies. The PSDFT approach can effectively remove the bright
foreground contamination and extract the targeted IM signals using a Bayesian
approach in a power-spectrum subspace. This new approach can be directly
applied to a broad range of IM analyses and will be well suited to future
high-quality IM datasets, providing a powerful tool for future IM surveys.Comment: 5 pages, 3 figure
Cross correlation surveys with the Square Kilometre Array
By the time that the first phase of the Square Kilometre Array is deployed it
will be able to perform state of the art Large Scale Structure (LSS) as well as
Weak Gravitational Lensing (WGL) measurements of the distribution of matter in
the Universe. In this chapter we concentrate on the synergies that result from
cross-correlating these different SKA data products as well as external
correlation with the weak lensing measurements available from CMB missions. We
show that the Dark Energy figures of merit obtained individually from WGL/LSS
measurements and their independent combination is significantly increased when
their full cross-correlations are taken into account. This is due to the
increased knowledge of galaxy bias as a function of redshift as well as the
extra information from the different cosmological dependences of the
cross-correlations. We show that the cross-correlation between a spectroscopic
LSS sample and a weak lensing sample with photometric redshifts can calibrate
these same photometric redshifts, and their scatter, to high accuracy by
modelling them as nuisance parameters and fitting them simultaneously
cosmology. Finally we show that Modified Gravity parameters are greatly
constrained by this cross-correlations because weak lensing and redshift space
distortions (from the LSS survey) break strong degeneracies in common
parameterisations of modified gravity.Comment: 12 pages, 3 figures. This article is part of the 'Cosmology Chapter,
Advancing Astrophysics with the SKA (AASKA14) Conference, Giardini Naxos
(Italy), June 9th-13th 2014
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