The VIMOS Public Extragalactic Redshift Survey (VIPERS) Never mind the gaps: comparing techniques to restore homogeneous sky coverage

Aims. Non-uniform sampling and gaps in sky coverage are common in galaxy redshift surveys, but these effects can degrade galaxy counts-in-cells measurements and density estimates. We carry out a comparative study of methods that aim to fill the gaps to correct for the systematic effects. Our study is motivated by the analysis of the VIMOS Public Extragalactic Redshift Survey (VIPERS), a flux-limited survey at i(AB) < 22.5 consisting of single-pass observations with the VLT Visible Multi-Object Spectrograph (VIMOS) with gaps representing 25% of the surveyed area and an average sampling rate of 35%. However, our findings are generally applicable to other redshift surveys with similar observing strategies. Methods. We applied two algorithms that use photometric redshift information and assign redshifts to galaxies based upon the spectroscopic redshifts of the nearest neighbours. We compared these methods with two Bayesian methods, the Wiener filter and the Poisson-Lognormal filter. Using galaxy mock catalogues we quantified the accuracy and precision of the counts-in-cells measurements on scales of R = 5 h(-1) Mpc and 8 h(-1) Mpc after applying each of these methods. We further investigated how these methods perform to account for other sources of uncertainty typical of spectroscopic surveys, such as the spectroscopic redshift error and the sparse, inhomogeneous sampling rate. We analysed each of these sources separately, then all together in a mock catalogue that mimicks the full observational strategy of a VIPERS-like survey. Results. In a survey such as VIPERS, the errors in counts-in-cells measurements on R < 10 h(-1) Mpc scales are dominated by the sparseness of the sample due to the single-pass observing strategy. All methods under-predict the counts in high-density regions by 20-35%, depending on the cell size, method, and underlying overdensity. This systematic bias is similar to random errors. No method outperforms the others: differences are not large, and methods with the smallest random errors can be more affected by systematic errors than others. Random and systematic errors decrease with the increasing size of the cell. All methods can effectively separate under-dense from over-dense regions by considering cells in the 1st and 5th quintiles of the probability distribution of the observed counts. Conclusions. We show that despite systematic uncertainties, it is possible to reconstruct the lowest and highest density environments on scales of 5 h(-1) Mpc at moderate redshifts 0.5 less than or similar to z less than or similar to 1.1, over a large volume such as the one covered by the VIPERS survey. This is vital for characterising cosmic variance and rare populations (e.g, brightest galaxies) in environmental studies at these redshifts.