Impacts of the physical data model on the forward inference of initial
  conditions from biased tracers
  We investigate the impact of each ingredient in the employed physical data
model on the Bayesian forward inference of initial conditions from biased
tracers at the field level. Specifically, we use dark matter halos in a given
cosmological simulation volume as tracers of the underlying matter density
field. We study the effect of tracer density, grid resolution, gravity model,
bias model and likelihood on the inferred initial conditions. We find that the
cross-correlation coefficient between true and inferred phases reacts weakly to
all ingredients above, and is well predicted by the theoretical expectation
derived from a Gaussian model on a broad range of scales. The bias in the
amplitude of the inferred initial conditions, on the other hand, depends
strongly on the bias model and the likelihood. We conclude that the bias model
and likelihood hold the key to an unbiased cosmological inference. Together
they must keep the systematics -- which arise from the sub-grid physics that
are marginalized over -- under control in order to obtain an unbiased
inference.
