The VIMOS Public Extragalactic Redshift Survey (VIPERS). Never mind the
  gaps: comparing techniques to restore homogeneous sky coverage
  [Abridged] Non-uniform sampling and gaps in sky coverage are common in galaxy
redshift surveys, but these effects can degrade galaxy counts-in-cells and
density estimates. We carry out a comparison of methods that aim to fill the
gaps to correct for the systematic effects. Our study is motivated by the
analysis of the VIMOS Extragalactic Redshift Survey (VIPERS), a flux-limited
survey (i<22.5) based on one-pass observations with VIMOS, with gaps covering
25% of the surveyed area and a mean sampling rate of 35%. Our findings are
applicable to other surveys with similar observing strategies. We compare 1)
two algorithms based on photometric redshift, that assign redshifts to galaxies
based on the spectroscopic redshifts of the nearest neighbours, 2) two Bayesian
methods, the Wiener filter and the Poisson-Lognormal filter. Using galaxy mock
catalogues we quantify the accuracy of the counts-in-cells measurements on
scales of R=5 and 8 Mpc/h after applying each of these methods. We also study
how they perform to account for spectroscopic redshift error and inhomogeneous
and sparse sampling rate. We find that in VIPERS the errors in counts-in-cells
measurements on R<10 Mpc/h scales are dominated by the sparseness of the
sample. All methods underpredict by 20-35% the counts at high densities. This
systematic bias is of the same order as random errors. No method outperforms
the others. Random and systematic errors decrease for larger cells. We show
that it is possible to separate the lowest and highest densities on scales of 5
Mpc/h at redshifts 0.5<z<1.1, over a large volume such as in VIPERS survey.
This is vital for the characterisation of cosmic variance and rare populations
(e.g, brightest galaxies) in environmental studies at these redshifts.
