This likelihood / bias model is implemented in libLSS/samplers/borg/borg_poisson_likelihood.cpp

Likelihood model

The likelihood is given by the Poisson model: {$$ P(N^g | \rho_g) = \frac{1}{N^g!} \mathrm{e}^{-\rho_g} \rho_g^{N^g} $$} where each 3d grid elements holding the {%N^g%} galaxies are supposed to be statistically independent realizations of the galaxy field {$\rho_g$}.

Bias model

The galaxy density {$\rho^g$} is derived from the dark matter field {$\rho^m$} using the following relation: {$$ \rho^g = A ({\rho_m})^{\alpha} \exp{} \left(-B (\rho^m)^{-\epsilon} \right) $$} with {$A$}, {$B$} and {$\epsilon$} free parameters.