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 4.

Numerical stability of each statistic.

Statistics	No	100	1000
(Results are log₁₀)	noise	hours	hours
$ϕ_{3 D}^{PS}$ $\phi^{\mathrm{PS}}_{\mathrm{3D}}$	−12.25	−12.20	−12.51
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{PS}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{PS}}$	−11.87	−9.24	−10.14
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{PS}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{PS}$	−11.57	−9.13	−9.11
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{WM}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WM}}$	−10.66	−8.92	−7.97
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{WM}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WM}}$	−11.20	−8.64	−9.14
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{m}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_m}$	−10.28	−7.17	−10.03
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{m}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_m}$	−10.08	−7.73	−7.38
${\bar{ϕ}}_{ℓ^{2} : 1, 2, 3, 4}^{{WST}_{w}}$ $\bar{\phi}_{\ell^2:1,2,3,4}^{\mathrm{WST}_w}$	−10.23	−9.16	−9.70
${\bar{ϕ}}_{ℓ^{1}, ℓ^{2} : 1, 2}^{{WST}_{w}}$ $\bar{\phi}_{\ell^1,\ell^2:1,2}^{\mathrm{WST}_w}$	−10.40	−8.88	−9.80

Notes. Looking at the numerical stability of the different statistics, we multiply the inverse of the covariance by the covariance, which should be an identity matrix. We show the largest off-diagonal term, as a test for numerical stability.

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