Bottom part: one extremely metal-poor star spectra of RAVE. The metallicity of this star was estimated by our study to be [Fe/H] = −3.04 ± 0.22 dex and the measured S/N per pixel is ~ 52. The gray box marks the region around the central Ca ii line for which the two solutions and their difference are plotted above. The gray shaded areas give ± 1σ Voigt profile solutions for the regular χ² approach (top) and the noise-modeled approach (bottom) with measured equivalent widths of the lines given next to each solution. In the latter case there is also a full model ± 1σ region shown in red (see text for details). The inset shows 20 draws from each of the three Gaussian process kernel posteriors using Eq. (9). The second and third group are vertically shifted by 0.1 and 0.2 for clarity.