Comparison of likelihood models with a noise-free mock data vector from the anisotropic systematics forward model. Shown are marginalised posterior contours: in blue, assuming the anisotropic systematics model within the standard setup of KiDS-SBI as described in Sect. 5.4; in black, assuming the same anisotropic systematics forward simulations to train a Mixture Density Network (MDN; Bishop 1994) which is made up of a single multivariate Gaussian; and in pink, applying a standard analysis which assumes a Gaussian likelihood characterised by a numerical sample covariance derived from anisotropic systematics forward simulations and a model given by the analytic pseudo-Cl model described in Appendix D. All posteriors are evaluated assuming the same noise realisation and the same model parameters (see Table E.1).