Fewer simulations, sharper covariances: Reducing mock covariance noise with Zeldovich approximation control variates
Abstract
We present a control-variate method for reducing the variance of power spectrum covariance matrix estimates from simulations of large-scale structure. The idea is to pair each mock simulation with a cheap Zeldovich-approximation realization sharing the same initial conditions, and to use the known statistical properties of the Zeldovich field to remove correlated sample variance from the covariance estimator. Under a Gaussian disconnected approximation, we derive fully analytic expressions for both the optimal control-variate coefficient, β(k,ℓ;k',ℓ'), and the corresponding correlation, ρ(k,ℓ;k',ℓ'), in terms of the auto- and cross-power spectra of the target and control fields. In the monopole case, the correlation takes the simple form ρ(k,k') = r2(k),r2(k'), where r(k) is the standard cross-correlation coefficient between the target and Zeldovich fields, implying that covariance estimation remains highly efficient whenever the two fields are strongly correlated. For masked redshift-space lognormal mocks, resembling LRGs from DESI, we find that the control-variate estimator reduces the variance of the covariance matrix by approximately an order of magnitude on large scales, k≲ 0.05 h Mpc−1, precisely where accurate covariance estimation is most challenging. The gains are smaller for higher k but typically accelerate convergence by a factor of 2-3, substantially lowering the computational cost of covariance estimation for current and upcoming large-scale structure surveys. After a cheap parametric-bootstrap calibration of the precision-matrix bias, the control-variate covariance yields a χ2 distribution consistent with the expected number of degrees of freedom. This method is readily implementable in current imaging and spectroscopic surveys (e.g., DESI, \textit{Euclid}, LSST, PFS, \textit{SPHEREx}).
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BibTeX
@misc{hadzhiyska2026fewer,
title = {{Fewer simulations, sharper covariances: Reducing mock covariance noise with Zeldovich approximation control variates}},
author = {Boryana Hadzhiyska and Martin White},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.28817},
eprint = {2605.28817},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.28817},
}
RIS
TY - UNPB
TI - Fewer simulations, sharper covariances: Reducing mock covariance noise with Zeldovich approximation control variates
AU - Boryana Hadzhiyska
AU - Martin White
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2605.28817
UR - https://arxiv.org/abs/2605.28817
AB - We present a control-variate method for reducing the variance of power spectrum covariance matrix estimates from simulations of large-scale structure. The idea is to pair each mock simulation with a cheap Zeldovich-approximation realization sharing the same initial conditions, and to use the known statistical properties of the Zeldovich field to remove correlated sample variance from the covariance estimator. Under a Gaussian disconnected approximation, we derive fully analytic expressions for both the optimal control-variate coefficient, β(k,ℓ;k',ℓ'), and the corresponding correlation, ρ(k,ℓ;k',ℓ'), in terms of the auto- and cross-power spectra of the target and control fields. In the monopole case, the correlation takes the simple form ρ(k,k') = r^2(k),r^2(k'), where r(k) is the standard cross-correlation coefficient between the target and Zeldovich fields, implying that covariance estimation remains highly efficient whenever the two fields are strongly correlated. For masked redshift-space lognormal mocks, resembling LRGs from DESI, we find that the control-variate estimator reduces the variance of the covariance matrix by approximately an order of magnitude on large scales, k≲ 0.05 h Mpc^−1, precisely where accurate covariance estimation is most challenging. The gains are smaller for higher k but typically accelerate convergence by a factor of 2-3, substantially lowering the computational cost of covariance estimation for current and upcoming large-scale structure surveys. After a cheap parametric-bootstrap calibration of the precision-matrix bias, the control-variate covariance yields a χ^2 distribution consistent with the expected number of degrees of freedom. This method is readily implementable in current imaging and spectroscopic surveys (e.g., DESI, \textit{Euclid}, LSST, PFS, \textit{SPHEREx}).
ER -