Bispectrum covariance in the flat-sky limit

Joachimi, Benjamin; Shi, Xun; Schneider, Peter

doi:10.1051/0004-6361/200912906

Cited by 37 publications

(37 citation statements)

References 21 publications

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“…In this paper we studied the range of applicability of the Gaussian approximation for the bispectrum covariance, as derived by Joachimi et al (2009), for non-Gaussian fields. We chose log-normal random fields as representative for nonGaussian fields motivated by the fact that the one-dimensional probability density function of the density fluctuations and the one-dimensional probability density function of the cosmic shear convergence field as well as the covariance of the power spectrum of cosmic shear fields are well described by the log-normal ansatz.…”

Section: Discussionmentioning

confidence: 99%

The bispectrum covariance beyond Gaussianity

Martín

Schneider

Simon

2012

A&A

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Context. To investigate and specify the statistical properties of cosmological fields with particular attention to possible non-Gaussian features, accurate formulae for the bispectrum and the bispectrum covariance are required. The bispectrum is the lowest-order statistic providing an estimate for non-Gaussianities of a distribution, and the bispectrum covariance depicts the errors of the bispectrum measurement and their correlation on different scales. Currently, there do exist fitting formulae for the bispectrum and an analytical expression for the bispectrum covariance, but the former is not very accurate and the latter contains several intricate terms and only one of them can be readily evaluated from the power spectrum of the studied field. Neglecting all higher-order terms results in the Gaussian approximation of the bispectrum covariance. Aims. We study the range of validity of this Gaussian approximation for two-dimensional non-Gaussian random fields. Methods. For this purpose, we simulate Gaussian and non-Gaussian random fields, the latter represented by log-normal fields and obtained directly from the former by a simple transformation. From the simulated fields, we calculate the power spectra, the bispectra, and the covariance from the sample variance of the bispectra, for different degrees of non-Gaussianity α, which is equivalent to the skewness on a given angular scale θ g . In doing so, we minimize sample variance by selecting the same "phases" of the Gaussian and non-Gaussian fields. Results. We find that the Gaussian approximation of the bispectrum covariance provides a good approximation for degrees of nonGaussianity α ≤ 0.5 and a reasonably accurate approximation for α ≤ 1, both on scales > ∼ 8θ g . For larger values of α, the Gaussian approximation clearly breaks down. Using results from cosmic shear simulations, we estimate that the cosmic shear convergence fields are described by α < ∼ 0.7 at θ g ∼ 4 .Conclusions. We therefore conclude that the Gaussian approximation for the bispectrum covariance is likely to be applicable in ongoing and future cosmic shear studies.

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Section: Discussionmentioning

confidence: 99%

The bispectrum covariance beyond Gaussianity

Martín

Schneider

Simon

2012

A&A

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“…refs. [6,78,79]), to our knowledge, the covariance matrix for the bispectrum has not been computed from simulations directly. Such a numerical calculation is beyond the scope of the present work, as well, and will be performed elsewhere.…”

Section: B Comparison To Bispectrummentioning

confidence: 99%

Probing cosmology with weak lensing Minkowski functionals

et al. 2012

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In this paper, we show that Minkowski Functionals (MFs) of weak gravitational lensing (WL) convergence maps contain significant non-Gaussian, cosmology-dependent information. To do this, we run a large suite of cosmological ray-tracing N-body simulations to create mock weak WL convergence maps, and study the cosmological information content of MFs derived from these maps. Our suite consists of 80 independent 512 3 N-body runs, covering seven different cosmologies, varying three cosmological parameters Ωm, w, and σ8 one at a time, around a fiducial ΛCDM model. In each cosmology, we use ray-tracing to create a thousand pseudo-independent 12 deg 2 convergence maps, and use these in a Monte Carlo procedure to estimate the joint confidence contours on the above three parameters. We include redshift tomography at three different source redshifts zs = 1, 1.5, 2, explore five different smoothing scales θG = 1, 2, 3, 5, 10 arcmin, and explicitly compare and combine the MFs with the WL power spectrum. We find that the MFs capture a substantial amount of information from non-Gaussian features of convergence maps, i.e. beyond the power spectrum. The MFs are particularly well suited to break degeneracies and to constrain the dark energy equation of state parameter w (by a factor of ≈ three better than from the power spectrum alone). The non-Gaussian information derives partly from the one-point function of the convergence (through V0, the "area" MF), and partly through non-linear spatial information (through combining different smoothing scales for V0, and through V1 and V2, the boundary length and genus MFs, respectively). In contrast to the power spectrum, the best constraints from the MFs are obtained only when multiple smoothing scales are combined.

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“…Noting that the bispectrum is only non‐zero if its three arguments can form the sides of a triangle (see e.g. Joachimi et al 2009 for details), we assemble the data vector out of all such combinations, where ℓ 1 , ℓ 2 and ℓ 3 can have 20 logarithmically spaced values between 10 and 1000.…”

Section: An Application: Breaking Degeneracies In the ωM–σ8 Planementioning

confidence: 99%

Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

Joachimi¹,

Taylor²

2011

Monthly Notices of the Royal Astronomical Society

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Forecasts of statistical constraints on model parameters using the Fisher matrix abound in many fields of astrophysics. The Fisher matrix formalism involves the assumption of Gaussianity in parameter space and hence fails to predict complex features of posterior probability distributions. Combining the standard Fisher matrix with Box-Cox transformations, we propose a novel method that accurately predicts arbitrary posterior shapes. The Box-Cox transformations are applied to parameter space to render it approximately multivariate Gaussian, performing the Fisher matrix calculation on the transformed parameters. We demonstrate that, after the Box-Cox parameters have been determined from an initial likelihood evaluation, the method correctly predicts changes in the posterior when varying various parameters of the experimental setup and the data analysis, with marginally higher computational cost than a standard Fisher matrix calculation. We apply the Box-Cox-Fisher formalism to forecast cosmological parameter constraints by future weak gravitational lensing surveys. The characteristic non-linear degeneracy between matter density parameter and normalisation of matter density fluctuations is reproduced for several cases, and the capabilities of breaking this degeneracy by weak lensing three-point statistics is investigated. Possible applications of Box-Cox transformations of posterior distributions are discussed, including the prospects for performing statistical data analysis steps in the transformed Gaussianised parameter space.Comment: 14 pages, 7 figures; minor changes to match version published in MNRA

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Bispectrum covariance in the flat-sky limit

Cited by 37 publications

References 21 publications

The bispectrum covariance beyond Gaussianity

The bispectrum covariance beyond Gaussianity

Probing cosmology with weak lensing Minkowski functionals

Forecasts of non-Gaussian parameter spaces using Box-Cox transformations

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