KiDS-SBI: Simulation-based inference analysis of KiDS-1000 cosmic shear

We present a simulation-based inference (SBI) cosmological analysis of cosmic shear two-point statistics from the fourth weak gravitational lensing data release of the ESO Kilo-Degree Survey (KiDS-1000). KiDS-SBI efficiently performs non-Limber projection of the matter power spectrum via Levin's method and constructs log-normal random matter fields on the curved sky for arbitrary cosmologies, including effective prescriptions for intrinsic alignments and baryonic feedback. The forward model samples realistic galaxy positions and shapes, based on the observational characteristics of KiDS-1000. It incorporates shear measurement and redshift calibration uncertainties, as well as angular anisotropies due to variable survey depth and point spread function (PSF) variations. To enable direct comparisons with standard inference, we limited our analysis to pseudo-angular power spectra as summary statistics. Here, the SBI is based on neural density estimation of the likelihood with active learning to infer the posterior distribution of spatially flat Lambda CDM cosmological parameters from 18 000 realisations. We inferred a mean marginal for the growth of the structure parameter of S8 equivalent to sigma 8(Omega m/0.3)0.5 = 0.731 +/- 0.033 (68%). We present a measurement of the goodness-of-fit for SBI, determining that the forward model fits the data well, with a probability-to-exceed of 0.42. For a fixed cosmology, the learnt likelihood is approximately Gaussian, while its constraints are wider, compared to a Gaussian likelihood analysis due to the cosmology dependence in the covariance. Neglecting variable depth and anisotropies in the point spread function in the model can cause S8 to be overestimated by similar to 5%. Our results are in agreement with previous analyses of KiDS-1000 and reinforce a 2.9 sigma tension with early Universe constraints from cosmic microwave background measurements. This work highlights the importance of forward-modelling systematic effects in upcoming galaxy surveys, such as Euclid, Rubin, and Roman.