Informed total-error-minimizing priors: Interpretable cosmological parameter constraints despite complex nuisance effects

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Volume 693 (January 2025)

A&A, 693 (2025) A178

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Table 2.

Ranges of the original and ITEM priors for the α model with a maximum bias of 0.4σ_2D and a minimum coverage of 56% for both Ω_m and S₈.

Parameter	Prior	Prior width	Bias [σ_2D]	Ω_m coverage	S₈ coverage	${\bar{σ}}_{Ω_{m}}$ $\overline{\sigma}_{\Omega_m}$	${\bar{σ}}_{S_{8}}$ $\overline{\sigma}_{S_8}$	$\tilde{V} / {\tilde{V}}_{Original}$ $\tilde{V}/\tilde{V}_{\mathrm{Original}}$
Original priors
α₀	𝒰[0.1, 3.0]	2.9	0.32/0.42	76%/76%	72%/52%	0.052	0.068	1.00
α₁	𝒰[–1.0, 4.0]	5.0	0.32/0.42	76%/76%	72%/52%	0.052	0.068	1.00

ITEM prior
α₀	𝒰[0.6, 2.0]	1.4	0.33/0.39	80%/64%	68%/56%	0.040	0.049	0.58
α₁	𝒰[–1.0, 1.1]	2.1	0.33/0.39	80%/64%	68%/56%	0.040	0.049	0.58

Notes. The bias and error coverage quantities from both nuisance realizations are illustrated for each prior as non-stochasticity/Buzzard stochasticity cases respectively. In the final three columns, we include the average error of the final estimate for Ω_m and S₈ from both nuisance realizations and the 2D approximated, normalized and re-scaled volume of the 2D marginalized posterior $\tilde{V}$ $\tilde{V}$ defined in Sect. 2.3.3.

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