Toward a robust inference method for the galaxy bispectrum: likelihood
  function and model selection
  The forthcoming generation of galaxy redshift surveys will sample the
large-scale structure of the Universe over unprecedented volumes with
high-density tracers. This advancement will make robust measurements of
three-point clustering statistics possible. In preparation for this
improvement, we investigate how several methodological choices can influence
inferences based on the bispectrum about galaxy bias and shot noise. We first
measure the real-space bispectrum of dark-matter haloes extracted from 298
N-body simulations covering a volume of approximately $1000 h^{-3}
\mathrm{Gpc}^3$. We then fit a series of theoretical models based on tree-level
perturbation theory to the numerical data. To achieve this, we estimate the
covariance matrix of the measurement errors by using 10,000 mock catalogues
generated with the Pinocchio code. We study how the model constraints are
influenced by the binning strategy for the bispectrum configurations and by the
form of the likelihood function. We also use Bayesian model-selection
techniques to single out the optimal theoretical description of our data. We
find that a three-parameter bias model combined with Poissonian shot noise is
necessary to model the halo bispectrum up to scales of $k_\mathrm{max}\lesssim
0.08 h \mathrm{Mpc}^{-1}$, although fitting formulae that relate the bias
parameters can be helpful to reduce the freedom of the model without
compromising accuracy. Our data clearly disfavour local Eulerian and local
Lagrangian bias models and do not require corrections to Poissonian shot noise.
We anticipate that model-selection diagnostics will be particularly useful to
extend the analysis to smaller scales as, in this case, the number of model
parameters will grow significantly large.
