Sample variance in weak lensing: How many simulations are required?

Journal Article · Thu Mar 24 00:00:00 EDT 2016 · Physical Review D

DOI: https://doi.org/10.1103/PhysRevD.93.063524 · OSTI ID:1245392

Petri, Andrea ^[1]; May, Morgan ^[2]; Haiman, Zoltan ^[3]

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1. Columbia Univ., New York, NY (United States); Brookhaven National Lab. (BNL), Upton, NY (United States)
2. Brookhaven National Lab. (BNL), Upton, NY (United States)
3. Columbia Univ., New York, NY (United States)

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 ray-tracing N-body 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 shear-shear power spectra and peak counts, we show that cubic and quartic covariance fluctuations lead to additional O(1/N²_r) error degradation that is not negligible when N_r is only a factor of few larger than N_b. We study the large N_r limit, and find that a single, 240 Mpc/h sized 512³-particle N-body simulation (N_s = 1) can be repeatedly recycled to produce as many as N_r = few × 10⁴ shear maps whose power spectra and high-significance peak counts can be treated as statistically independent. Lastly, a small number of simulations (N_s = 1 or 2) is sufficient to forecast parameter confidence intervals at percent accuracy.

• Research Organization: Brookhaven National Laboratory (BNL), Upton, NY (United States)
• Sponsoring Organization: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• OSTI ID: 1245392
• Report Number(s): BNL--111951-2016-JA; KA2301020
• Journal Information: Physical Review D, Journal Name: Physical Review D Journal Issue: 6 Vol. 93; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical Society (APS)Copyright Statement
• Country of Publication: United States
• Language: English