SBI posteriors (red for true covariance $\hat{\mathrm{\Sigma }}=\mathrm{\Sigma }$, blue for simulation-estimated covariance $\hat{\mathrm{\Sigma }}=S$, used in the compression of Eq. 12) derived with Neural Posterior fits from a set of repeated experiments for each value of the number of simulations n_s using a CNF model (left) and a MAF model (right). Each panel is for a different random realization 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 $\hat{\mathit{\xi }}$ linearly compressed to summaries $\hat{\mathit{\pi }}$ and are shown in red and blue. A Fisher forecast at true parameters π with the true data covariance Σ is shown with a dotted black line.