Histogram of the prediction errors of the Likelihood_emulator for the relxillp model (with the mean and the standard deviation of the error). From 50 000 drawing posterior samples derived from the fifth inference round, 50 000 exact likelihoods were used for training the neural network. 5000 additional likelihood samples were used for the test set and compared with the predictions from the Likelihood_emulator. The accuracy reached is sufficient for performing accurately the importance sampling correction.