SBI posteriors (red for $\hat{\mathrm{\Sigma }}=\mathrm{\Sigma }$, blue for $\hat{\mathrm{\Sigma }}=S$, used in the compression of Eq. 12) derived with Neural Likelihood fits from a set of repeated experiments for each value of the number of simulations n_s using a CNF (left) and a MAF (right) model. Each panel is for a different random set of data $\hat{\mathit{\xi }}$ and covariance S drawn from Gaussian and Wishart distributions respectively. For each flow and value of n_s, independent datavectors $\hat{\mathit{\xi }}$ are linearly compressed to summaries $\hat{\mathit{x}}$ and are shown in red and blue. A Fisher forecast at true parameters π with the true data covariance Σ is shown in black.