Average model parameter posterior variance reported by methods compared in this work, conditioned on noisy data vectors estimated with neural-likelihood estimation using a masked autoregressive flow. The colour-coded dashed lines show the (Fisher) variances that would have been measured if the exact data covariance had been known and used in a Gaussian likelihood ansatz with a flat prior. Cross points label posterior variances from SBI analyses where the exact data covariance was known for linear compression (Eq. (12)). Dotted lines show the expected variances of the maximum a posteriori that would have been measured when using a data covariance estimated from a set of n_s simulations. Note that these lines multiply the Fisher variance with the factor (Eq. (7)) Dodelson & Schneider (2013) calculated using 2 × n_s simulations. Circle points label posterior variances from SBI analyses where the data covariance was estimated from n_s simulations and used in a linear compression. Diamond points label posterior variances obtained when using a compression with the diagonal elements of the estimated covariance matrix. Square points show variances obtained using a neural network for the compression, trained on n_s simulations. All points include a 1-σ error bar on the variances estimated over all of the experiments. The additional simulations, not labelled on the x-axis but required for the separate compressions (where the true covariance is unknown), are noted for each method. When the true data covariance is not known, necessitating the use of double the number of simulations, the reconstructed posterior errors from SBI are significantly higher than the Dodelson & Schneider (2013) corrected errors when that correction is substantial.