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We present a comparison of major methodologies of fast generating mock haloor galaxy catalogues. The comparison is done for two-point and the three-pointclustering statistics. The reference catalogues are drawn from the BigMultiDarkN-body simulation. Both friend-of-friends (including distinct halos only) andspherical overdensity (including distinct halos and subhalos) catalogs havebeen used with the typical number density of a large-volume galaxy surveys. Wedemonstrate that a proper biasing model is essential for reproducing the powerspectrum at quasilinear and even smaller scales. With respect to variousclustering statistics a methodology based on perturbation theory and arealistic biasing model leads to very good agreement with N-body simulations.However, for the quadrupole of the correlation function or the power spectrum,only the method based on semi-N-body simulation could reach high accuracy (1%level) at small scales, i.e., r<25 Mpc/h or k>0.15 h/Mpc. Full N-body solutionswill remain indispensable to produce reference catalogues. Nevertheless, wehave demonstrated that the far more efficient approximate solvers can reach afew percent accuracy in terms of clustering statistics at the scalesinteresting for the large-scale structure analysis after calibration with a fewreference N-body calculations. This makes them useful for massive productionaimed at covariance studies, to scan large parameter spaces, and to estimateuncertainties in data analysis techniques, such as baryon acoustic oscillationreconstruction, redshift distortion measurements, etc.

nIFTy Cosmology: Galaxy/halo mock catalogue comparison project on clustering statistics