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 $\ge 10$) 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 $\sim 5$. 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