Sample Variance

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Jun'ichi Yokoyama - One of the best experts on this subject based on the ideXlab platform.

  • Sample Variance of the Higher-Order Cumulants of the Cosmic Velocity Divergence Field
    Publications of the Astronomical Society of Japan, 2000
    Co-Authors: Naoki Seto, Jun'ichi Yokoyama
    Abstract:

    If primordial fluctuations follow Gaussian distribution, higher-order cumulants of cosmic fields could reflect nonlinear mode coupling, and would provide useful information about the gravitational instability picture of structure formation. We show that, in the usual case that the observed Sample has a limited volume, their expected deviation (Sample Variance) from their universal values is nonvanishing, even in linear theory. As a result, we find that the relative Sample Variance of the skewness of the velocity divergence field can be as large as ~ 30% in current velocity surveys.

  • Sample Variance of the cosmic velocity field
    The Astrophysical Journal, 1998
    Co-Authors: Naoki Seto, Jun'ichi Yokoyama
    Abstract:

    Since the cosmic peculiar velocity field depends strongly on small wavenumber modes, we cannot probe its universal properties unless we observe a sufficiently large region. We calculate the expected deviation (Sample Variance) of the peculiar velocity dispersion from its universal value in the case where the observed volume is finite. Using linear theory, we show that the Sample Variance remains as large as ~10%, even if the observed region is as deep as 100 h-1 Mpc, and that it seriously affects the estimation of cosmological parameters from the peculiar velocity field.

Risa H Wechsler - One of the best experts on this subject based on the ideXlab platform.

  • Sample Variance in photometric redshift calibration cosmological biases and survey requirements
    Monthly Notices of the Royal Astronomical Society, 2012
    Co-Authors: Dragan Huterer, C E Cunha, M T Busha, Risa H Wechsler
    Abstract:

    We use N-body/photometric galaxy simulations to examine the impact of Sample Variance of spectroscopic redshift Samples on the accuracy of photometric redshift (photo-z) determination and calibration of photo-z errors. We estimate the biases in the cosmological parameter constraints from weak lensing and derive requirements on the spectroscopic follow-up for three different photo-z algorithms chosen to broadly span the range of algorithms available. We find that Sample Variance is much more relevant for the photo-z error calibration than for photo-z training, implying that follow-up requirements are similar for different algorithms. We demonstrate that the spectroscopic Sample can be used for training of photo-zs and error calibration without incurring additional bias in the cosmological parameters. We provide a guide for observing proposals for the spectroscopic follow-up to ensure that redshift calibration biases do not dominate the cosmological parameter error budget. For example, assuming optimistically (pessimistically) that the weak lensing shear measurements from the Dark Energy Survey could obtain 1σ constraints on the dark energy equation of state w of 0.035 (0.055), implies a follow-up requirement of 150 (40) patches of sky with a telescope such as Magellan, assuming a 1/8 deg2 effective field of view and 400 galaxies per patch. Assuming (optimistically) a VIMOS-VLT Deep Survey-like spectroscopic completeness with purely random failures, this could be accomplished with about 75 (20) nights of observation. For more realistic assumptions regarding spectroscopic completeness, or with the presence of other sources of systematics not considered here, further degradations to dark energy constraints are possible. We test several approaches for making the requirements less stringent. For example, if the redshift distribution of the overall Sample can be estimated by some other technique, e.g. cross-correlation, then follow-up requirements could be reduced by an order of magnitude.

G M Bernstein - One of the best experts on this subject based on the ideXlab platform.

  • propagating Sample Variance uncertainties in redshift calibration simulations theory and application to the cosmos2015 data
    Monthly Notices of the Royal Astronomical Society, 2020
    Co-Authors: C Sanchez, Marco Raveri, Alex Alarcon, G M Bernstein
    Abstract:

    Cosmological analyses of galaxy surveys rely on knowledge of the redshift distribution of their galaxy Sample. This is usually derived from a spectroscopic and/or many-band photometric calibrator survey of a small patch of sky. The uncertainties in the redshift distribution of the calibrator Sample include a contribution from shot noise, or Poisson sampling errors, but, given the small volume they probe, they are dominated by Sample Variance introduced by large-scale structures. Redshift uncertainties have been shown to constitute one of the leading contributions to systematic uncertainties in cosmological inferences from weak lensing and galaxy clustering, and hence they must be propagated through the analyses. In this work, we study the effects of Sample Variance on small-area redshift surveys, from theory to simulations to the COSMOS2015 data set. We present a three-step Dirichlet method of resampling a given survey-based redshift calibration distribution to enable the propagation of both shot noise and Sample Variance uncertainties. The method can accommodate different levels of prior confidence on different redshift sources. This method can be applied to any calibration Sample with known redshifts and phenotypes (i.e. cells in a self-organizing map, or some other way of discretizing photometric space), and provides a simple way of propagating prior redshift uncertainties into cosmological analyses. As a worked example, we apply the full scheme to the COSMOS2015 data set, for which we also present a new, principled SOM algorithm designed to handle noisy photometric data. We make available a catalog of the resulting resamplings of the COSMOS2015 galaxies.

Naoki Seto - One of the best experts on this subject based on the ideXlab platform.

  • Sample Variance of the Higher-Order Cumulants of the Cosmic Velocity Divergence Field
    Publications of the Astronomical Society of Japan, 2000
    Co-Authors: Naoki Seto, Jun'ichi Yokoyama
    Abstract:

    If primordial fluctuations follow Gaussian distribution, higher-order cumulants of cosmic fields could reflect nonlinear mode coupling, and would provide useful information about the gravitational instability picture of structure formation. We show that, in the usual case that the observed Sample has a limited volume, their expected deviation (Sample Variance) from their universal values is nonvanishing, even in linear theory. As a result, we find that the relative Sample Variance of the skewness of the velocity divergence field can be as large as ~ 30% in current velocity surveys.

  • Sample Variance of the cosmic velocity field
    The Astrophysical Journal, 1998
    Co-Authors: Naoki Seto, Jun'ichi Yokoyama
    Abstract:

    Since the cosmic peculiar velocity field depends strongly on small wavenumber modes, we cannot probe its universal properties unless we observe a sufficiently large region. We calculate the expected deviation (Sample Variance) of the peculiar velocity dispersion from its universal value in the case where the observed volume is finite. Using linear theory, we show that the Sample Variance remains as large as ~10%, even if the observed region is as deep as 100 h-1 Mpc, and that it seriously affects the estimation of cosmological parameters from the peculiar velocity field.

Xiao-chun Luo - One of the best experts on this subject based on the ideXlab platform.

  • Sample Variance of non-Gaussian sky distributions
    The Astrophysical Journal, 1995
    Co-Authors: Xiao-chun Luo
    Abstract:

    Non-Gaussian distributions of cosmic microwave background (CMB) anisotropies has been proposed to reconcile the discrepancies between different experimental at half-degree scales. Each experiment probes a different part of the sky, furthermore, sky coverage is very small, hence the Sample Variance of each experiment can be large, especially when the sky signal is non-Gaussian. We model the degree-scale CMB sky as a $\chi_{n}~{2}$ field with $n$-degrees of freedom and show that the Sample Variance is enhanced over Gaussian distribution by a factor of $ {(n +6)/ n}$. The Sample Variance for different experiments are calculated, both for Gaussian or non-Gaussian distributions. We will also show that if the distribution is highly non-Gaussian at half-degree scale $(n \ltwid 4)$, then non-Gaussian signatures of the CMB could be detected in the FIRS map, though probably not in the COBE map.

  • Sample Variance of non-Gaussian Sky Distributions
    The Astrophysical Journal, 1995
    Co-Authors: Xiao-chun Luo
    Abstract:

    Non-Gaussian distributions of cosmic microwave background (CMB) anisotropies have been proposed to reconcile the discrepancies between different experiments at half-degree scales (Coulson et al. 1994). Each experiment probes a different part of the sky, furthermore, sky coverage is very small, hence the Sample Variance of each experiment can be large, especially when the sky signal is non-Gaussian. We model the degree-scale CMB sky as a $\chi_{n}^{2}$ field with $n$-degrees of freedom and show that the Sample Variance is enhanced over that of a Gaussian distribution by a factor of $ {(n +6)/ n}$. The Sample Variance for different experiments are calculated, both for Gaussian and non-Gaussian distributions. We also show that if the distribution is highly non-Gaussian $(n \ltwid 4)$ at half-degree scales, then the non-Gaussian signature of the CMB could be detected in the FIRS map, though probably not in the COBE map.