Table 3.
Predictions for the variance of the covariance estimate, based on the covariance of covariance for PINOCCHIO mocks.
| Cost |  |
iFoM | ||||||
|---|---|---|---|---|---|---|---|---|
| M | Δr | Smp | LC | Smp | LC | Smp | LC | Ratio |
| 10 | 1 | 31 | 7 | 1.151 | 1.852 | 35.7 | 13.0 | 2.8 |
| 2 | 1.124 | 1.582 | 34.8 | 11.1 | 3.1 | |||
| 5 | 1.106 | 1.400 | 34.3 | 9.8 | 3.5 | |||
| 10 | 1.102 | 1.328 | 34.2 | 9.3 | 3.7 | |||
| 20 | 1.102 | 1.283 | 34.1 | 9.0 | 3.8 | |||
| 20 | 1 | 61 | 7 | 1.082 | 1.871 | 66.0 | 13.1 | 5.0 |
| 2 | 1.076 | 1.591 | 65.6 | 11.1 | 5.9 | |||
| 5 | 1.073 | 1.404 | 65.5 | 9.8 | 6.7 | |||
| 10 | 1.076 | 1.331 | 65.7 | 9.3 | 7.0 | |||
| 20 | 1.081 | 1.284 | 65.9 | 9.0 | 7.3 | |||
| 50 | 1 | 151 | 7 | 1.041 | 1.883 | 157 | 13.1 | 11.9 |
| 2 | 1.048 | 1.597 | 158 | 11.1 | 14.1 | |||
| 5 | 1.054 | 1.407 | 159 | 9.8 | 16.2 | |||
| 10 | 1.061 | 1.332 | 160 | 9.3 | 17.2 | |||
| 20 | 1.068 | 1.285 | 161 | 9.0 | 17.9 | |||
| 100 | 1 | 301 | 7 | 1.028 | 1.887 | 309 | 13.2 | 23.4 |
| 2 | 1.038 | 1.599 | 313 | 11.2 | 27.9 | |||
| 5 | 1.048 | 1.408 | 315 | 9.9 | 32.0 | |||
| 10 | 1.056 | 1.333 | 318 | 9.3 | 34.1 | |||
| 20 | 1.064 | 1.286 | 320 | 9.0 | 35.6 | |||
Notes. Sample covariance (Smp) and LC covariance with Ma = 1 are compared. The columns are: size of random catalog, parametrized as M = Nr/Nd; bin size Δr in units of h−1 Mpc; computational cost of pair counting per realization, in units of the pair count cost of the data catalog; 
, variance of the covariance estimate per bin for N = 2 realizations and for distance scales 20–200 h−1 Mpc; inverse figure-of-merit, product of 
and computational cost; ratio of sample-covariance iFoM to that of the LC.
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