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 3.

Condition number of the statistics.

Statistics	No	100	1000
(Results are log₁₀)	noise	hours	hours
$ϕ_{3 D}^{PS}$ $\phi^{\mathrm{PS}}_{\mathrm{3D}}$	4.46	4.33	4.28
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{PS}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{PS}}$	5.03	6.52	6.21
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{PS}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{PS}$	5.08	6.49	6.17
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{WM}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WM}}$	6.17	8.10	7.62
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{WM}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WM}}$	5.47	8.04	7.6
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{m}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_m}$	6.14	9.03	8.9
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{m}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_m}$	6.12	8.98	8.86
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{w}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_w}$	6.19	7.66	6.92
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{w}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_w}$	6.21	7.56	6.92

Notes. To ensure the robustness of our statistical analysis, it is important to assess the condition numbers of the various statistics – which have all been whitened – employed in this paper under different noise treatments. A condition number below or of the order of 10⁷ is generally considered indicative of a well-conditioned covariance matrix.

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