KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis

We present the methodology for a joint cosmological analysis of weak gravitational lensing from the fourth data release of the ESO Kilo-Degree Survey (KiDS-1000) and galaxy clustering from the partially overlapping Baryon Oscillation Spectroscopic Survey (BOSS) and the 2-degree Field Lensing Survey (2dFLenS). Cross-correlations between BOSS and 2dFLenS galaxy positions and source galaxy ellipticities have been incorporated into the analysis, necessitating the development of a hybrid model of non-linear scales that blends perturbative and non-perturbative approaches, and an assessment of signal contributions by astrophysical effects. All weak lensing signals were measured consistently via Fourier-space statistics that are insensitive to the survey mask and display low levels of mode mixing. The calibration of photometric redshift distributions and multiplicative gravitational shear bias has been updated, and a more complete tally of residual calibration uncertainties was propagated into the likelihood. A dedicated suite of more than 20 000 mocks was used to assess the performance of covariance models and to quantify the impact of survey geometry and spatial variations of survey depth on signals and their errors. The sampling distributions for the likelihood and the chi(2) goodness-of-fit statistic have been validated, with proposed changes for calculating the effective number of degrees of freedom. The prior volume was explicitly mapped, and a more conservative, wide top-hat prior on the key structure growth parameter S-8=sigma(8) (Omega(m)/0.3)(1/2) was introduced. The prevalent custom of reporting S-8 weak lensing constraints via point estimates derived from its marginal posterior is highlighted to be easily misinterpreted as yielding systematically low values of S-8, and an alternative estimator and associated credible interval are proposed. Known systematic effects pertaining to weak lensing modelling and inference are shown to bias S-8 by no more than 0.1 standard deviations, with the caveat that no conclusive validation data exist for models of intrinsic galaxy alignments. Compared to the previous KiDS analyses, S-8 constraints are expected to improve by 20% for weak lensing alone and by 29% for the joint analysis.