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Table 1

Parameter constraints obtained from the MCMC-based analysis for different scenarios.

Cases Parameters Prior Input Mean 68% Limits 95% Limits Best-fit
100 FRBs log(ζo) [0, ∞] 1.079 0.86 [0.57, 1.04] [0.45, 1.35] 1.07
α [–20, 20] 1.4 3.53 [1.73, 5.52] [0.19, 6.74] 1.39
log TΓe (in K) [3, 7] 4.279 4.77 [3.43, 5.70] [3, 7] 4.42
τe 0.0547 0.0530 [0.0505,0.0546] [0.0491,0.0580] 0.0547
∆ɀ 2.275 1.79 [1.19,2.14] [0.93,2.90] 2.33
ɀmid 7.168 7.19 [7.00,7.34] [6.88,7.54] 7.18
500 FRBs log(ζ0) [0, ∞] 1.079 0.96 [0.76,1.16] [0.55,1.33] 1.20
α [–20, 20] 1.4 2.6 [0.91,3.67] [0.15,5.65] 1.06
log Tre (in K) [3,7] 4.279 4.75 [3.78,5.83] [3,6.11] 3.78
τe 0.0547 0.0537 [0.0518,0.0551] [0.0506,0.0571] 0.0553
∆ɀ 2.275 2.03 [1.56,2.41] [1.27,2.87] 2.29
ɀmid 7.168 7.20 [7.08,7.31] [7.00,7.43] 7.16
1000 FRBs log(ζ0) [0, ∞] 1.079 1.02 [0.84,1.16] [0.73,1.38] 1.07
α [–20, 20] 1.4 2.04 [0.95,2.80] [0.27,4.06] 1.44
log Tre (in K) [3, 7] 4.279 4.69 [3.85,5.69] [3,5.92] 4.32
τe 0.0547 0.0543 [0.0528,0.0554] [0.0518,0.0569] 0.0547
∆ɀ 2.275 2.18 [1.87,2.46] [1.60,2.79] 2.27
ɀmid 7.168 7.22 [7.11,7.31] [7.04,7.41] 7.17
only 21 cm log(ζ0) [0, ∞] 1.079 1.16 [1.00,1.26] [0.95,1.43] 1.13
α [-20, 20] 1.4 1.09 [0.60,1.46] [0.38,1.89] 1.10
log Tre (in K) [3,7] 4.279 4.07 [3.64,4.67] [3,4.84] 4.17
τe 0.0547 0.0550 [0.0544,0.0557] [0.0538,0.0560] 0.0550
∆ɀ 2.275 2.41 [2.28,2.52] [2.20,2.64] 2.39
ɀmid 7.168 7.14 [7.10,7.19] [7.05,7.23] 7.15
1000 FRBs + 21 cm log(ζ0) [0, ∞] 1.079 1.10 [0.99,1.17] [0.94,1.32] 1.09
α [-20, 20] 1.4 1.31 [0.92,1.68] [0.65,1.97] 1.30
log Tre (in K) [3,7] 4.279 4.28 [3.96,4.72] [3.42,5.00] 4.30
τe 0.0547 0.0549 [0.0542,0.0554] [0.0538,0.0559] 0.0548
∆ɀ 2.275 2.34 [2.25,2.41] [2.19,2.49] 2.33
ɀmid 7.168 7.17 [7.14,7.20] [7.12,7.23] 7.17

Notes. For each case, the first three rows correspond to the free parameters of the model, and the remaining three are the derived parameters. The free parameters are assumed to have uniform priors with the ranges listed in the third column. The other columns show the input value for the mock generation and the recovered posterior mean value along with the 68% and 95% confidence limits on different parameters. The best-fit values are quoted in the last column.

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