Diagnosing systematic effects using the inferred initial power spectrum

Open Access

Table 1.

Main variables, their generic role in the statistical framework, and their physical interpretation in this study.

Symbol	Role in the BHM	Physical meaning in this work
ω ∈ ℝ^N	Target parameters	Cosmological parameters h, Ω_m, Ω_b, n_S and σ₈, corresponding to N = 5.
θ ∈ ℝ^S	Latent vector	Vectorial parametrisation of the initial matter power spectrum over S = 64 support points.
ψ ∈ ℝ^T	Nuisance parameters	Random numbers involved in the phase and noise realisations.
o ∈ ℝ^N	Target parameters treated as nuisance parameters	Cosmological parameters h, Ω_m, Ω_b, n_S and σ₈ at play inside the probabilistic simulator 𝒫(Φ\|θ), which is the second part of the BHM, used for the latent vector inference. The symbol o is introduced to avoid confusion with ω in the first part of the BHM.
d ∈ ℝ^D	Full data vector	Three-dimensional maps of the galaxy number counts in the survey volume for the three mock populations of galaxies. D = 3 ⋅ 512³ ≃ 4 × 10⁸.
Φ ∈ ℝ^P	Summary statistics	Power spectra of the galaxy number count fields. We use the concatenation of the three 27-dimensional estimated power spectra for each galaxy population, so P = 111.
Φ_O ∈ ℝ^P	Observed summary statistics	Power spectra of the observed galaxy number count fields. The capital letter “O” stands for “Observations”.
$\tilde{ω} \in R^{N}$ $\boldsymbol{\widetilde{\omega}} \in \mathbb{R}^N$	Compressed summaries	Summary statistics of the galaxy number count fields after data compression.

Notes. The variables’ roles within the BHM are defined in Section 2.1. We elaborate upon their physical interpretations in Section 3, which describes the large-scale spectroscopic galaxy survey model used in this study.

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