Wavelet-based statistics for enhanced 21cm EoR parameter constraints

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Volume 686 (June 2024)

A&A, 686 (2024) A212

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Table 5.

No noise case, Cramer-Rao bounds.

Statistics	T_Vir	R_Max	ζ
(Results are log₁₀)
$ϕ_{3 D}^{PS}$ $\phi^{\mathrm{PS}}_{\mathrm{3D}}$	7.42	2.01	1.50
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{PS}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{PS}}$	7.25	2.05	1.37
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{PS}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{PS}}$	7.13	2.04	1.28
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{WM}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WM}}$	5.45	0.93	−0.22
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{WM}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WM}}$	6.25	1.00	0.43
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{m}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_m}$	6.00	0.98	0.27
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{m}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_m}$	5.99	1.01	0.30
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{w}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_w}$	5.81	0.58	−0.07
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{w}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_w}$	5.79	0.60	−0.05

Notes. Cramer-Rao bounds for all of our summary statistics in the case where we have no noise. The bound establishes a lower bound on the variance, i.e. the smallest uncertainty achievable for an unbiased estimate on a given parameter.

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