Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum

We compare the measurements of the bispectrum and the estimate of its covariance obtained from a set of different methods for the efficient generation of approximate dark matter halo catalogues to the same quantities obtained from full N-body simulations. To this purpose we employ a large set of 300 realizations of the same cosmology for each method, run with matching initial conditions in order to reduce the contribution of cosmic variance to the comparison. In addition, we compare how the error on cosmological parameters such as linear and non-linear bias parameters depends on the approximate method used for the determination of the bispectrum variance. As general result, most methods provide errors within 10 per cent of the errors estimated from N-body simulations. Exceptions are those methods requiring calibration of the clustering amplitude but restrict this to 2-point statistics. Finally we test how our results are affected by being limited to a few hundreds measurements from N-body simulation by comparing with a larger set of several thousands of realizations performed with one approximate method.