KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear

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Volume 694 (February 2025)

A&A, 694 (2025) A223

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Table 2.

Parameters that are varied within the simulation-based inference pipeline and their priors.

Parameter	Symbol	Prior type	Prior range	Initial fiducial	Final fiducial
Density fluctuation amp.	S₈	Flat	[0.1, 1.3]	0.760	0.739
Hubble constant	h₀	Flat	[0.64, 0.82]	0.767	0.653
Cold dark matter density	ω_c	Flat	[0.051, 0.255]	0.118	0.135
Baryonic matter density	ω_b	Flat	[0.019, 0.026]	0.026	0.023
Scalar spectral index	n_s	Flat	[0.84, 1.1]	0.901	0.972

Intrinsic alignment amp.	A_IA	Flat	[–6, 6]	0.264	0.603
Baryon feedback amp.	A_bary	Flat	[2, 3.13]	3.10	2.66
Redshift displacement	δ_z	Gaussian	𝒩(0, C_z)	0	0

Multiplicative shear bias	M^(p)	Gaussian	$N ({\bar{M}}^{(p)}, σ_{M}^{(p)})$ $\mathcal{N}(\overline{M}^{(p)}, \sigma^{(p)}_{M})$	${\bar{M}}^{(p)}$ $\overline{M}^{(p)}$	${\bar{M}}^{(p)}$ $\overline{M}^{(p)}$
Additive shear bias	$c_{1, 2}^{(p)}$ $c_{1,2}^{(p)}$	Gaussian	$N ({\bar{c}}_{1, 2}^{(p)}, σ_{c_{1, 2}}^{(p)})$ $\mathcal{N}(\overline{c}_{1,2}^{(p)}, \sigma^{(p)}_{c_{1,2}})$	${\bar{c}}_{1, 2}^{(p)}$ $\overline{c}_{1,2}^{(p)}$	${\bar{c}}_{1, 2}^{(p)}$ $\overline{c}_{1,2}^{(p)}$
PSF variation shear bias	$α_{1, 2}^{(p)}$ $\alpha_{1,2}^{(p)}$	Gaussian	$N ({\bar{α}}_{1, 2}^{(p)}, σ_{α_{1, 2}}^{(p)})$ $\mathcal{N}(\overline{\alpha}_{1,2}^{(p)}, \sigma^{(p)}_{\alpha_{1,2}})$	${\bar{α}}_{1, 2}^{(p)}$ $\overline{\alpha}_{1,2}^{(p)}$	${\bar{α}}_{1, 2}^{(p)}$ $\overline{\alpha}_{1,2}^{(p)}$

Notes. The prior ranges are selected to be exactly in line with previous KiDS-1000 analyses (Asgari et al. 2021; Heymans et al. 2021; Loureiro et al. 2022; van den Busch et al. 2022; Tröster et al. 2022). The upper five rows show the cosmological parameters of interest, while the three rows below show the nuisance parameters which quantify systematic biases. The last three rows show shear bias parameters for each tomographic bin, p, as given in Fig. 5 which are sampled implicitly within each simulation by drawing from the prior distribution, so any posterior is pre-marginalised over these parameters. For flat priors, the lower and upper limits of the normalised rectangular function defines the prior. For the Gaussian prior on δ_z, we use a 5D multivariate Gaussian with its mean at the zero vector and the covariance, C_z, defined by the one estimated in Hildebrandt et al. (2021). We note that for simplicity, the δ_z are implicitly marginalised throughout this analysis. The fiducial values given here constitute the fiducial parameter choice for the score compression described in Sect. 5.3.

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