tokens: the maximal error is roughly 6 times smaller than this upper limit. Table 2. In this table we compare nonlinear correction spectra computed with EuclidEmulator (EE) on the one hand and with an emulator based on Takahashi’s HALOFIT (THF) on the other hand to nonlinear correction spectra of full N -body simulations for 36 cosmologies outside the ED over the entire k and range. The numbers in the table correspond to the relative errors in per cent between the emulated and simulated nonlinear corrections. We find that the errors predicted with the THF emulator are broadly consistent with the EE errors. This implies that the configuration of the EE based on a HALOFIT emulator is actually valid and that there is no need to make a huge investment to run N -body simulations just for the configuration study of an emulator. This result is particularly important for finding the size of the ED (see Fig. 5 ). 4.2 Sensitivity analysis Sobol’ indices (Sobol’ 1993 , 2001 ) measure how sensitive the eigenvalues λ i (ω b , ω m , n s , h , 0 , σ 8 ) (introduced in equation 9 ) are to each single input parameter as well as to any of their interactions. For an introduction into Sobol’ sensitivity analysis, we refer to the previous references or to Marelli et al. ( 2017 ) and Le Gratiet, Marelli Sudret ( 2016 ). Sobol’ indices are based on the Hoeffding-Sobol’ decomposition, which states that any square-integrable function over a hypercube input parameter space can be cast as a sum of a constant, a set of univariate functions of each input parameter, another set of bivariate functions, etc. This decomposition is unique and the various terms are orthogonal with each other (with respect to the uniform probability measure over the hypercube). The variance of the output can then be apportioned to each input parameter, each pair, triplets, etc.: these contributions are called Sobol’ sensitivity indices S . Although their classical estimation relies on costly Monte Carlo simulations, Sobol’ indices can be computed analytically from a PCE as in equation ( 9 ), see Sudret ( 2008 ). In our case, we get one such Sobol’ expansion for each principal component. Each Sobol’ index corresponds to the fraction of the total variance of the respective eigenvalue that is caused by the parameter(s) under consideration. The bigger this number, the more λ i depends on the considered set of input parameters. Fig. 7 shows the first-order (no interactions) Sobol’ index plots for the first and fifth principal components (see Fig. A1 in Appendix A ). It is interesting to notice that the input parameter ω b has no leading-order effect on the output nonlinear correction. The nonlinear correction starts to show non-vanishing sensitivity to this parameter only at fifth order and higher. This is explained by the fact that baryons are treated as a background quantity that only come into the simulation data via the transfer function. As they are not directly evolved themselves in PKDGRAV3 , their
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