Sample variance in weak lensing: How many simulations are required?
Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension N _{b} with its simulated counterpart. An accurate estimate of the N _{b} × N _{b} feature covariance matrix C is essential to obtain accurate parameter confidence intervals. When C is measured from a set of simulations, an important question is how large this set should be. To answer this question, we construct different ensembles of N _{r} realizations of the shear field, using a common randomization procedure that recycles the outputs from a smaller number N _{s} ≤ N _{r} of independent raytracing Nbody simulations. We study parameter confidence intervals as a function of (N _{s}, N _{r}) in the range 1 ≤ N _{s} ≤ 200 and 1 ≤ N _{r} ≲ 105. Previous work [S. Dodelson and M. D. Schneider, Phys. Rev. D 88, 063537 (2013)] has shown that Gaussian noise in the feature vectors (from which the covariance is estimated) lead, at quadratic order, to an O(1/N _{r}) degradation of the parameter confidence intervals. Using a variety of lensing features measured in our simulations, including shearshear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead tomore »
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Columbia Univ., New York, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
 Brookhaven National Lab. (BNL), Upton, NY (United States)
 Columbia Univ., New York, NY (United States)
 Publication Date:
 Report Number(s):
 BNL1119512016JA
Journal ID: ISSN 24700010; PRVDAQ; KA2301020
 Grant/Contract Number:
 SC00112704; AC0298CH10886; SC0012704; ACI1053575
 Type:
 Accepted Manuscript
 Journal Name:
 Physical Review D
 Additional Journal Information:
 Journal Volume: 93; Journal Issue: 6; Journal ID: ISSN 24700010
 Publisher:
 American Physical Society (APS)
 Research Org:
 Brookhaven National Laboratory (BNL), Upton, NY (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), High Energy Physics (HEP) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS
 OSTI Identifier:
 1245392
 Alternate Identifier(s):
 OSTI ID: 1243154
Petri, Andrea, May, Morgan, and Haiman, Zoltan. Sample variance in weak lensing: How many simulations are required?. United States: N. p.,
Web. doi:10.1103/PhysRevD.93.063524.
Petri, Andrea, May, Morgan, & Haiman, Zoltan. Sample variance in weak lensing: How many simulations are required?. United States. doi:10.1103/PhysRevD.93.063524.
Petri, Andrea, May, Morgan, and Haiman, Zoltan. 2016.
"Sample variance in weak lensing: How many simulations are required?". United States.
doi:10.1103/PhysRevD.93.063524. https://www.osti.gov/servlets/purl/1245392.
@article{osti_1245392,
title = {Sample variance in weak lensing: How many simulations are required?},
author = {Petri, Andrea and May, Morgan and Haiman, Zoltan},
abstractNote = {Constraining cosmology using weak gravitational lensing consists of comparing a measured feature vector of dimension Nb with its simulated counterpart. An accurate estimate of the Nb × Nb feature covariance matrix C is essential to obtain accurate parameter confidence intervals. When C is measured from a set of simulations, an important question is how large this set should be. To answer this question, we construct different ensembles of Nr realizations of the shear field, using a common randomization procedure that recycles the outputs from a smaller number Ns ≤ Nr of independent raytracing Nbody simulations. We study parameter confidence intervals as a function of (Ns, Nr) in the range 1 ≤ Ns ≤ 200 and 1 ≤ Nr ≲ 105. Previous work [S. Dodelson and M. D. Schneider, Phys. Rev. D 88, 063537 (2013)] has shown that Gaussian noise in the feature vectors (from which the covariance is estimated) lead, at quadratic order, to an O(1/Nr) degradation of the parameter confidence intervals. Using a variety of lensing features measured in our simulations, including shearshear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead to additional O(1/N2r) error degradation that is not negligible when Nr is only a factor of few larger than Nb. We study the large Nr limit, and find that a single, 240 Mpc/h sized 5123particle Nbody simulation (Ns = 1) can be repeatedly recycled to produce as many as Nr = few × 104 shear maps whose power spectra and highsignificance peak counts can be treated as statistically independent. Lastly, a small number of simulations (Ns = 1 or 2) is sufficient to forecast parameter confidence intervals at percent accuracy.},
doi = {10.1103/PhysRevD.93.063524},
journal = {Physical Review D},
number = 6,
volume = 93,
place = {United States},
year = {2016},
month = {3}
}