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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 $R_p$.