Mean and standard deviation of the inferred non-linearly evolved density fields, computed from the MCMC realizations, with the same slice through the 3D fields being depicted above for both the Poissonian (upper panels) and augmented (lower panels) likelihoods. The filamentary nature of the non-linearly evolved density field can be observed in the regions constrained by the data, with the unobserved or masked regions displaying larger uncertainty, as expected. Unlike our robust data model, the standard Poissonian analysis yields some artefacts in the reconstructed density field, particularly near the edges of the survey, where the foreground contamination is stronger.