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 catalogs to the same quantities
obtained from full N-body simulations. To this purpose we employ a large set of
three-hundred realisations 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 nonlinear bias parameters depends on
the approximate method used for the determination of the bispectrum variance.
As general result, most methods provide errors within 10% of the errors
estimated from N-body simulations. Exceptions are those methods requiring
calibration of the clustering amplitude but restrict this to two-point
statistics. Finally we test how our results are affected by being limited to a
few hundreds measurements from N-body simulation, and therefore to the
bispectrum variance, by comparing with a larger set of several thousands
realisations performed with one approximate method.
