Table 1.
Fraction of simulations crossing the 3σ threshold (i.e., ℱ3σ given in percent). The total number of simulations is 1000.
| Fvar | AI | |||||||
|---|---|---|---|---|---|---|---|---|
| Sim | TS | W | No-cut | Soft-cut | Hard-cut | No-cut | Soft-cut | Hard-cut |
| (1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) |
| Sim-null (sanity check) | Averaged | ⌀W 3R | 0.1% | 0.3% | 0.1% | 0.1% | 0.1% | 0.4% |
| Averaged | ⌀W 1R | 0.2% | 0.2% | 0.2% | 0.2% | 0.2% | 0.5% | |
| Counted | ⌀W 3R | 0.0% | 0.1% | 0.2% | 0.1% | 0.4% | 0.1% | |
| Counted | ⌀W 1R | 0.2% | 0.2% | 0.3% | 0.1% | 0.3% | 0.1% | |
| Averaged | WG 3R | 0.3% | 0.4% | 0.3% | 0.1% | 0.1% | 0.0% | |
| Averaged | WT 1R | 0.2% | 0.1% | 0.3% | 0.5% | 0.4% | 0.5% | |
| Counted | WG 3R | 0.3% | 0.3% | 0.3% | 0.1% | 0.1% | 0.1% | |
| Counted | WT 1R | 0.3% | 0.3% | 0.5% | 0.3% | 0.6% | 0.1% | |
| Sim-best (special-case) | Averaged | ⌀W 3R | 0.2% | 0.4% | 0.5% | 0.3% | 0.1% | 0.7% |
| Averaged | ⌀W 1R | 0.2% | 0.6% | 0.6% | 0.4% | 0.2% | 0.6% | |
| Counted | ⌀W 3R | 0.0% | 0.4% | 2.2% | 0.4% | 1.1% | 4.7% | |
| Counted | ⌀W 1R | 0.3% | 0.5% | 4.7% | 0.4% | 1.2% | 8.8% | |
| Averaged | WG 3R | 89.6% | 89.1% | 84.4% | 83.6% | 83.8% | 83.7% | |
| Averaged | WT 1R | 5.9% | 6.3% | 2.8% | 2.2% | 2.3% | 2.0% | |
| Counted | WG 3R | 96.7% | 96.7% | 96.8% | 98.7% | 98.7% | 98.7% | |
| Counted | WT 1R | 8.4% | 9.3% | 20.1% | 24.0% | 25.3% | 47.4% | |
| Sim-mid (special-case) | Averaged | ⌀W 3R | 0.5% | 1.7% | 3.0% | 0.3% | 0.2% | 1.2% |
| Averaged | ⌀W 1R | 0.9% | 1.8% | 1.0% | 0.7% | 0.5% | 0.4% | |
| Counted | ⌀W 3R | 0.8% | 2.7% | 55.7% | 1.5% | 9.9% | 97.2% | |
| Counted | ⌀W 1R | 2.4% | 8.8% | 94.4% | 4.4% | 25.3% | 100.0% | |
| Averaged | WG 3R | 0.4% | 0.4% | 0.1% | 0.2% | 0.2% | 0.0% | |
| Averaged | WT 1R | 25.2% | 17.8% | 0.2% | 8.9% | 5.4% | 0.1% | |
| Counted | WG 3R | 0.8% | 0.8% | 0.8% | 0.4% | 0.4% | 0.2% | |
| Counted | WT 1R | 46.8% | 49.2% | 82.3% | 87.5% | 87.9% | 99.7% | |
| Sim-0.2𝒮 (realistic) | Averaged | ⌀W 3R | 1.8% | 4.2% | 1.7% | 0.6% | 0.6% | 0.6% |
| Averaged | ⌀W 1R | 3.9% | 7.4% | 0.6% | 0.5% | 0.7% | 0.4% | |
| Counted | ⌀W 3R | 5.0% | 14.2% | 24.8% | 16.7% | 44.2% | 55.6% | |
| Counted | ⌀W 1R | 15.6% | 43.2% | 55.1% | 36.9% | 81.7% | 80.3% | |
| Averaged | WG 3R | 53.6% | 50.0% | 31.8% | 46.8% | 42.9% | 27.9% | |
| Averaged | WT 1R | 58.9% | 41.7% | 2.1% | 26.6% | 14.8% | 1.0% | |
| Counted | WG 3R | 68.7% | 68.6% | 58.8% | 83.6% | 83.0% | 72.9% | |
| Counted | WT 1R | 84.8% | 84.8% | 69.7% | 97.8% | 97.5% | 88.4% | |
| Sim-𝒮 (sanity check) | Averaged | ⌀W 3R | 61.7% | 80.0% | 38.9% | 14.6% | 25.0% | 13.0% |
| Averaged | ⌀W 1R | 88.2% | 95.3% | 2.2% | 29.0% | 29.3% | 1.3% | |
| Counted | ⌀W 3R | 99.6% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| Counted | ⌀W 1R | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| Averaged | WG 3R | 100.0% | 100.0% | 98.8% | 97.5% | 97.8% | 95.5% | |
| Averaged | WT 1R | 100.0% | 100.0% | 13.5% | 88.9% | 77.7% | 7.1% | |
| Counted | WG 3R | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
| Counted | WT 1R | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | 100.0% | |
Notes. Column (1) refers to the sample of simulated blazars (see Sect. 3.1). Column (2) refers to the TS parameter (see Sect. 3.2); Averaged and Counted refer to the averaging-based and counting-based TS parameters, respectively. Column (3) refers to the weighting scheme as well as the neutrino error region size (see Sect. 3.3.1); ⌀W, WG, and WT imply no weighting, Gaussian weighting, and top-hat weighting, respectively; 1R and 3R indicate the neutrino error region edge is Rϕ and 3Rϕ, respectively. Columns (4) and (7) refer to the no-cut neutrino subsample, columns (5) and (8) refer to the soft-cut neutrino subsample, and columns (6) and (9) refer to the hard-cut neutrino subsample (see Sect. 3.3.2). In columns (4)–(6), Fvar is used as the variability measure; while in columns (7)–(9), AI is used as the variability measure.
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