Mitigating incoherent excess variance in high-redshift 21 cm observations with multi-output cross-Gaussian process regression

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Volume 704 (December 2025)

A&A, 704 (2025) A205

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Table 2

Covariance model used in GPR with linked hyperparameters for the two nights.


Kernel	Parm	Input	Prior	Posterior
Kernel	Parm	Input	Prior	Standard	Cross
K_int	σ²	−0.344	−1, 0	$- {0.344}_{- 0.018}^{+ 0.019}$ $\[-0.344_{-0.018}^{+0.019}\]$	$- {0.342}_{- 0.019}^{+ 0.017}$ $\[-0.342_{-0.019}^{+0.017}\]$
(RBF)	ℓ	27.171	20, 40	${26.684}_{- 0.751}^{+ 0.813}$ $\[26.684_{-0.751}^{+0.813}\]$	${26.880}_{- 0.815}^{+ 0.779}$ $\[26.880_{-0.815}^{+0.779}\]$
K_mix	σ²	−2.105	−2.5, −1.5	$- {2.101}_{- 0.006}^{+ 0.006}$ $\[-2.101_{-0.006}^{+0.006}\]$	$- {2.104}_{- 0.005}^{+ 0.005}$ $\[-2.104_{-0.005}^{+0.005}\]$
(RBF)	ℓ	0.503	0.1, 1	${0.505}_{- 0.002}^{+ 0.002}$ $\[0.505_{-0.002}^{+0.002}\]$	${0.504}_{- 0.001}^{+ 0.001}$ $\[0.504_{-0.001}^{+0.001}\]$
K₂₁	x₁	1	−4, 4	${1.083}_{- 2.034}^{+ 1.806}$ $\[1.083_{-2.034}^{+1.806}\]$	${1.658}_{- 0.544}^{+ 1.043}$ $\[1.658_{-0.544}^{+1.043}\]$
(VAE)	x₂	−0.5	−4, 4	${1.612}_{- 0.860}^{+ 1.142}$ $\[1.612_{-0.860}^{+1.142}\]$	$- {0.467}_{- 0.053}^{+ 0.093}$ $\[-0.467_{-0.053}^{+0.093}\]$
	σ²	−3.449	−5, −2	$- {4.387}_{- 0.128}^{+ 0.203}$ $\[-4.387_{-0.128}^{+0.203}\]$	$- {3.510}_{- 0.055}^{+ 0.039}$ $\[-3.510_{-0.055}^{+0.039}\]$
K_ex	σ²	−3.960	−5, −2	$- {3.568}_{- 0.088}^{+ 0.062}$ $\[-3.568_{-0.088}^{+0.062}\]$	$- {3.959}_{- 0.004}^{+ 0.004}$ $\[-3.959_{-0.004}^{+0.004}\]$
(Exp)	ℓ	0.251	0.1, 0.5	${0.414}_{- 0.085}^{+ 0.058}$ $\[0.414_{-0.085}^{+0.058}\]$	${0.253}_{- 0.003}^{+ 0.003}$ $\[0.253_{-0.003}^{+0.003}\]$

Notes. The prior column indicates the uniform prior bounds. The posterior column indicates the estimated median and 68% confidence intervals obtained with MCMC.

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