Illustration of the prior space in the likelihood analysis for cosmological parameters. The black dots are the 40 training cosmologies from AEMULUS suite. Since Box023 has an outlier value of σ ₈, we just use the other 39 models to get a covariance matrix of the cosmological parameters. Then we define a distance metric χ ² and only allow the sampling of the points within a threshold. This defines a 7D ellipsoid with uniform and uninformative distribution. The red dots show the resulting sampling in the prior space, i.e., the ellipsoid imposed with the range of each parameter as shown in the first section of Table 3.