Cosmology behind the mask: Constraining the parameters of $\Lambda$CDM
  with the unmasked galaxy density field from VIPERS
  Galaxy redshift surveys are designed to map cosmic structures in three
dimensions for large-scale structure studies. Nevertheless, limitations due to
sampling and the survey window are unavoidable and degrade the cosmological
constraints. We present an analysis of the VIMOS Public Extragalactic Redshift
Survey (VIPERS) over the redshift range $0.6 < z < 1$ that is optimised to
extract the cosmological parameters while fully accounting for the complex
survey geometry. We employ the Gibbs sampling algorithm to iteratively draw
samples of the galaxy density field in redshift space, the galaxy bias, the
matter density, baryon fraction and growth-rate parameter $f\sigma_8$ based on
a multivariate Gaussian likelihood and prior on the density field. Despite the
high number of degrees of freedom, the samples converge to the joint posterior
distribution and give self-consistent constraints on the model parameters. We
validate the approach using VIPERS mock galaxy catalogues. Although the
uncertainty is underestimated by the Gaussian likelihood on the scales that we
consider by 50 %, the dispersion of the results from the mock catalogues gives
a robust error estimate. We find that the precision of the results matches
those of the traditional analyses applied to the VIPERS data that use more
constrained models. By relaxing the model assumptions, we confirm that the data
deliver consistent constraints on the $\Lambda$CDM model. This work provides a
case-study for the application of maximum-likelihood analyses for the next
generation of galaxy redshift surveys.
