The bispectrum covariance beyond Gaussianity

Martín, S.; Schneider, Peter; Simon, Patrick

doi:10.1051/0004-6361/201118020

Cited by 11 publications

(10 citation statements)

References 22 publications

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“…In the case of third-order cosmic shear statistics, however, Simon et al (2015) recently have found, at least in current state-of-the-art surveys, that a Gaussian likelihood is a reasonably good approximation. This agrees with results for the bispectrum covariance put forward by Martin et al (2012). As an additional remark, objections against the use of Gaussian likelihoods as a "safe default" have been raised in cases where one lacks knowledge of the exact form of the likelihood, as pointed out, for example, in power spectrum analyses by Carron (2013) and Sun et al (2013).…”

Section: Introductionsupporting

confidence: 85%

Constrained correlation functions from the Millennium Simulation

Wilking

Röseler

Schneider

2015

A&A

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Context. In previous work, we developed a quasi-Gaussian approximation for the likelihood of correlation functions that incorporates fundamental mathematical constraints on correlation functions, in contrast to the usual Gaussian approach. The analytical computation of these constraints is only feasible in the case of correlation functions of one-dimensional random fields. Aims. In this work, we aim to obtain corresponding constraints in the case of higher dimensional random fields and test them in a more realistic context. Methods. We develop numerical methods of computing the constraints on correlation functions that are also applicable for twoand three-dimensional fields. To test the accuracy of the numerically obtained constraints, we compare them to the analytical results for the one-dimensional case. Finally, we compute correlation functions from the halo catalog of the Millennium Simulation, check whether they obey the constraints, and examine the performance of the transformation used in the construction of the quasi-Gaussian likelihood.Results. We find that our numerical methods of computing the constraints are robust and that the correlation functions measured from the Millennium Simulation obey them. Even though the measured correlation functions lie well inside the allowed region of parameter space, i.e., far away from the boundaries of the allowed volume defined by the constraints, we find strong indications that the quasi-Gaussian likelihood yields a substantially more accurate description than the Gaussian one.

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Section: Introductionsupporting

confidence: 85%

Constrained correlation functions from the Millennium Simulation

Wilking

Röseler

Schneider

2015

A&A

Self Cite

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“…Therefore we would like to correct this effect by multiplying a factor shown in Hartlap et al [44]. For N R independent simulations, an unbiased estimator of the inverse covariance is as follows [e.g., 44,45]: (29) for N R − 2 > p, where p is the number of bins in the spectra. For our tomographic analysis with l max = 2000, the dimensions of the resulting covariance matrices are 30 × 30, 345 × 345, and 375 × 375 for the power spectrum, bispectrum, and their joint covariance, respectively.…”

Section: Signal-to-noise Ratiomentioning

confidence: 99%

“…Only the first term in Equation ( 12) is usually discussed in previous statistical analyses of the cosmological fields in the literature [7,29] except for Kayo et al [17], just because of simplicity and/or difficulty of calculation of the last four terms (see [e.g., 30,31] for real-space analyses of third-order lensing measurements). We will carefully examine how well the approximation of Gaussianity (here, the word "Gaussianity" means that the covariance matrix of the power spectrum and bispectrum is described by only the first term of Equations 8 and 12) is valid for computing the bispectrum covariance and its impact on cosmological parameter estimations, by comparing with the fully nonlinear covariance matrix measured from a large ensemble of ray-tracing simulations.…”

Section: B Covariance Matrices Of the Lensing Power Spectrum And Bisp...mentioning

confidence: 99%

Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation

Sato

Nishimichi

2013

Phys. Rev. D

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We study how well the Gaussian approximation is valid for computing the covariance matrices of the convergence power and bispectrum in weak gravitational lensing analyses. We focus on its impact on the cosmological parameter estimations by comparing the results with and without nonGaussian error contribution in the covariance matrix. We numerically derive the covariance matrix as well as the cosmology dependence of the spectra from a large set of N -body simulations performed for various cosmologies and carry out Fisher matrix forecasts for tomographic weak lensing surveys with three source redshifts. After showing the consistency of the power and bispectra measured from our simulations with the state-of-the-art fitting formulas, we investigate the covariance matrix assuming a typical ongoing survey across 1500 deg 2 with the mean source number density of 30 arcmin −2 at the mean redshift zs = 1.0. Although the shape noise contributes a significant fraction to the total error budget and it mitigates the impact of the non-Gaussian error for this source number density, we find that the non-Gaussian error degrades the cumulative signal-to-noise ratio up to the maximum multipole of 2000 by a factor of about 2 (3) in the power (bi-) spectrum analysis. Its impact on the final cosmological parameter forecast with 6 parameters can be as large as 15% in the size of the one-dimensional statistical error. This can be a problem in future wide and deep weak lensing surveys for precision cosmology. We also show how much the dark energy figure of merit is affected by the non-Gaussian error contribution and demonstrate an optimal survey design with a fixed observational time.

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“…Skewness and kurtosis are commonly used to measure the signal Gaussian characteristic in the engineering field. 24,25 The skewness is the third-order moments of signal and the kurtosis is the fourth-order moments of signal.…”

Section: Methodsmentioning

confidence: 99%

Bispectrum-based sEMG multi-domain joint feature extraction for upper limb motion classification

Chen

Zhou

Cheng

et al. 2015

Proceedings of the Institution of Mechanical Engineers, Part C:

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sEMG based motion pattern recognition is the focus in the rehabilitation medical engineering area. In order to get more information to characterize the sEMG signal of different upper limb motions, the signal data acquisition program is designed and the non-Gaussian characteristic of the sEMG signal is analyzed, the result shows that the sEMG signal collected is non-Gaussian signal. Bispectrum as a third-order statistics contains non-Gaussian information and the integral of bispectrum slice is extracted as feature. After that, the PCA method is adopted to reduce the bispectrum feature dimension. Then, the integral of bispectrum slice after PCA and the integral value of sEMG are combined as a multi-domain joint feature called BisIE. Finally, the experiment is executed to validate the effectiveness of the feature extraction method proposed by the SVM classifier compared with power spectrum-based multi-domain joint feature MMIE. The average classification accuracy of BisIE is about 97% and that of MMIE is about 93%. Besides, for the same subject, the classification accuracy of BisIE is higher than that of MMIE. The result shows that the proposed feature BisIE is effective in promoting sEMG-based upper limb motion recognition accuracy.

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The bispectrum covariance beyond Gaussianity

Cited by 11 publications

References 22 publications

Constrained correlation functions from the Millennium Simulation

Constrained correlation functions from the Millennium Simulation

Impact of the non-Gaussian covariance of the weak lensing power spectrum and bispectrum on cosmological parameter estimation

Bispectrum-based sEMG multi-domain joint feature extraction for upper limb motion classification

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