Average model parameter posterior variance conditioned on noisy datavectors estimated with Neural Posterior Estimation using a masked autoregressive flow. The same marginal Fisher variances, DS13 factors and compression methods are used for this plot as in Fig. 2. These results depend on using Σ_r as the true covariance (see Sect. 5) for the data generating process. When the true data covariance is not known and has significant non-diagonal elements (r = 0.2; see Appendix F), the compression using either a neural network f_ψ or an estimate of the diagonal elements S_diag. of the covariance in a linear compression fails catastrophically.