Illustration of the inference of the halo environment distribution p(δ|g). Left: Galaxies traced back to their origin in Lagrangian space (marked as black dots) and with the (smoothed) linear density field, δ, inferred at their Lagrangian locations. Right: Environment distribution (orange histogram) given by the distribution of δ at the galaxy locations which is notably biased relative to the matter distribution, p(δ), (blue histogram and a Gaussian represented as dashed line). The galaxy environment distribution is well approximated through p(δ)f(δ), where here f(δ) is a quadratic polynomial bias function.