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

Andrea Petri; Zoltán Haiman; Morgan May

doi:10.1103/PhysRevD.93.063524

paper

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

arXiv:1601.06792 · doi:10.1103/PhysRevD.93.063524

Abstract

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 $N_{b} \times N_{b}$ 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 $N_{s} \leq N_{r}$ of independent ray-tracing $N$ --body simulations. We study parameter confidence intervals as a function of ( $N_{s}, N_{r}$ ) in the range $1 \leq N_{s} \leq 200$ and $1 \leq N_{r} ≲ 1 0^{5}$ . Previous work 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 $O (1/ N_{r}^{2})$ 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, 240Mpc $/ h$ sized $51 2^{3}$ -particle $N$ --body simulation ( $N_{s} = 1$ ) can be repeatedly recycled to produce as many as $N_{r} = few \times 1 0^{4}$ shear maps whose power spectra and high-significance peak counts can be treated as statistically independent. As a result, a small number of simulations ( $N_{s} = 1$ or $2$ ) is sufficient to forecast parameter confidence intervals at percent accuracy.

12 pages, 6 figures, 2 tables; PRD accepted

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

Abstract

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