The model implemented in ARES is the most simple 'linear' model. The density field is supposed to be a pure Gaussian random field, which linearly biased, selected and with a Gaussian error model. For a single catalog, the forward model corresponds to:

{$$\tag{1} N^\mathrm{g}_p = \bar{N} R_p (1 + b \delta_p) + n_p$$}

with {$$\langle n_p n_{p'} \rangle = R_p \bar{N} \delta^K_{p, p'},$$} {$\delta^K$} is the Kronecker symbol, {$R_p$} is the linear response of the survey, i.e. the 3d completeness, {$b$} the linear bias and {$\bar{N}$} the mean number of galaxies per grid element. Effectively {$\bar{N}$} will absorb the details of the normalization of {$R_p$}.