  Standard approaches to Bayesian parameter inference in large scale structure
assume a Gaussian functional form (chi-squared form) for the likelihood. This
assumption, in detail, cannot be correct. Likelihood free inferences such as
Approximate Bayesian Computation (ABC) relax these restrictions and make
inference possible without making any assumptions on the likelihood. Instead
ABC relies on a forward generative model of the data and a metric for measuring
the distance between the model and data. In this work, we demonstrate that ABC
is feasible for LSS parameter inference by using it to constrain parameters of
the halo occupation distribution (HOD) model for populating dark matter halos
with galaxies.
  Using specific implementation of ABC supplemented with Population Monte Carlo
importance sampling, a generative forward model using HOD, and a distance
metric based on galaxy number density, two-point correlation function, and
galaxy group multiplicity function, we constrain the HOD parameters of mock
observation generated from selected "true" HOD parameters. The parameter
constraints we obtain from ABC are consistent with the "true" HOD parameters,
demonstrating that ABC can be reliably used for parameter inference in LSS.
Furthermore, we compare our ABC constraints to constraints we obtain using a
pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD
parameter constraints. Ultimately our results suggest that ABC can and should
be applied in parameter inference for LSS analyses.
