177 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
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
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
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
The varying w spread spectrum effect for radio interferometric imaging
We study the impact of the spread spectrum effect in radio interferometry on
the quality of image reconstruction. This spread spectrum effect will be
induced by the wide field-of-view of forthcoming radio interferometric
telescopes. The resulting chirp modulation improves the quality of
reconstructed interferometric images by increasing the incoherence of the
measurement and sparsity dictionaries. We extend previous studies of this
effect to consider the more realistic setting where the chirp modulation varies
for each visibility measurement made by the telescope. In these first
preliminary results, we show that for this setting the quality of
reconstruction improves significantly over the case without chirp modulation
and achieves almost the reconstruction quality of the case of maximal, constant
chirp modulation.Comment: 1 page, 1 figure, Proceedings of the Biomedical and Astronomical
Signal Processing Frontiers (BASP) workshop 201
PkANN - II. A non-linear matter power spectrum interpolator developed using artificial neural networks
In this paper we introduce PkANN, a freely available software package for
interpolating the non-linear matter power spectrum, constructed using
Artificial Neural Networks (ANNs). Previously, using Halofit to calculate
matter power spectrum, we demonstrated that ANNs can make extremely quick and
accurate predictions of the power spectrum. Now, using a suite of 6380 N-body
simulations spanning 580 cosmologies, we train ANNs to predict the power
spectrum over the cosmological parameter space spanning confidence
level (CL) around the concordance cosmology. When presented with a set of
cosmological parameters ( and redshift ), the trained ANN interpolates the power
spectrum for at sub-per cent accuracy for modes up to
. PkANN is faster than computationally expensive
N-body simulations, yet provides a worst-case error per cent fit to the
non-linear matter power spectrum deduced through N-body simulations. The
overall precision of PkANN is set by the accuracy of our N-body simulations, at
5 per cent level for cosmological models with eV for all
redshifts . For models with eV, predictions are
expected to be at 5 (10) per cent level for redshifts (). The
PkANN interpolator may be freely downloaded from
http://zuserver2.star.ucl.ac.uk/~fba/PkANNComment: 21 pages, 14 figures, 2 table
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